View Full Version : wavelengths of macroscopic bodies
Charles J. Quarra
Aug12-04, 08:29 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nHi,\n\nFrequently, in introductory quantum mechanics books the relation\nbetween wavelength-momentum is used uncospicuously for macroscopic\nobjects, probably for didactic purposes, however i see a problem with\nthat extrapolation: if one would go on and adding the momenta of the\ncomposite objects to obtain a "body-momenta", then one should ask if\nwhy that cant extrapolate to, for example, light beams (as the one you\ngot on a laser). If there is a system in which one can fulfill the\ncondition of coherent constructive propagation is in the laser light.\nA laser pulse has a lot more total momenta than its constitutive\nphotons (each produced by an individual atom line) however one doesnt\nsee this "total momenta wavelength" at\nwork in the physics of these systems, at least nothing\nim aware.\n\nany insights about this?\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hi,
Frequently, in introductory quantum mechanics books the relation
between wavelength-momentum is used uncospicuously for macroscopic
objects, probably for didactic purposes, however i see a problem with
that extrapolation: if one would go on and adding the momenta of the
composite objects to obtain a "body-momenta", then one should ask if
why that cant extrapolate to, for example, light beams (as the one you
got on a laser). If there is a system in which one can fulfill the
condition of coherent constructive propagation is in the laser light.
A laser pulse has a lot more total momenta than its constitutive
photons (each produced by an individual atom line) however one doesnt
see this "total momenta wavelength" at
work in the physics of these systems, at least nothing
im aware.
any insights about this?
Doug Goncz
Aug13-04, 05:41 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n>From: disposablemailaccountfornews@yahoo.com.ar (Charles J. Quarra)\n\n>Message-ID: <bc979c06.0408091425.528ca2fa@posting.google.com>\ n\n(snip)\n\n>A laser pulse has a lot more total momenta than its constitutive\n>photons (each produced by an individual atom line) however one doesnt\n>see this "total momenta wavelength" at\n> work in the physics of these systems, at least nothing\n>im aware.\n\nMmm, does it? It\'s concentrated energy, but isn\'t momentum a conserved\nquantity?\n\n\nYours,\n\nDoug Goncz ( ftp://users.aol.com/DGoncz/incoming )\nStudent member SAE for one year.\nI love: Dona, Jeff, Kim, Mom, Neelix, Tasha, and Teri, alphabetically.\nI drive: A double-step Thunderbolt with 657% range.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>>From: disposablemailaccountfornews@yahoo.com.ar (Charles J. Quarra)
>Message-ID: <bc979c06.0408091425.528ca2fa@posting.google.com>
(snip)
>A laser pulse has a lot more total momenta than its constitutive
>photons (each produced by an individual atom line) however one doesnt
>see this "total momenta wavelength" at
> work in the physics of these systems, at least nothing
>im aware.
Mmm, does it? It's concentrated energy, but isn't momentum a conserved
quantity?
Yours,
Doug Goncz ( ftp://users.aol.com/DGoncz/incoming )
Student member SAE for one year.
I love: Dona, Jeff, Kim, Mom, Neelix, Tasha, and Teri, alphabetically.
I drive: A double-step Thunderbolt with 657% range.
Charles J. Quarra
Aug14-04, 06:58 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\ndgoncz@aol.com ( Doug Goncz ) wrote in message news:<20040812193746.05745.00002949@mb-m14.aol.com>...\n> >From: disposablemailaccountfornews@yahoo.com.ar (Charles J. Quarra)\n\n> >A laser pulse has a lot more total momenta than its constitutive\n> >photons (each produced by an individual atom line) however one doesnt\n> >see this "total momenta wavelength" at\n> > work in the physics of these systems, at least nothing\n> >im aware.\n>\n> Mmm, does it? It\'s concentrated energy, but isn\'t momentum a conserved\n> quantity?\n>\n\nwell, of course. Let me rephrase a little better what i said; a laser\npulse has a _total momenta_ a lot bigger than the individual momenta\nof any of its constitutive photons, however one doesnt see this "total\nmomenta wavelength" at work in the physics of these systems (i.e:\nlasers) at least nothing im aware of.\n\ngreetings\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>dgoncz@aol.com ( Doug Goncz ) wrote in message news:<20040812193746.05745.00002949@mb-m14.aol.com>...
> >From: disposablemailaccountfornews@yahoo.com.ar (Charles J. Quarra)
> >A laser pulse has a lot more total momenta than its constitutive
> >photons (each produced by an individual atom line) however one doesnt
> >see this "total momenta wavelength" at
> > work in the physics of these systems, at least nothing
> >im aware.
>
> Mmm, does it? It's concentrated energy, but isn't momentum a conserved
> quantity?
>
well, of course. Let me rephrase a little better what i said; a laser
pulse has a _total momenta_ a lot bigger than the individual momenta
of any of its constitutive photons, however one doesnt see this "total
momenta wavelength" at work in the physics of these systems (i.e:
lasers) at least nothing im aware of.
greetings
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n\n\n\n"Charles J. Quarra" <disposablemailaccountfornews@yahoo.com.ar> wrote in message\nnews:bc979c06.0408091425.528ca2fa@posting .google.com...\n>\n>\n> Hi,\n>\n> Frequently, in introductory quantum mechanics books the relation\n> between wavelength-momentum is used uncospicuously for macroscopic\n> objects, probably for didactic purposes, however i see a problem with\n> that extrapolation: if one would go on and adding the momenta of the\n> composite objects to obtain a "body-momenta", then one should ask if\n> why that cant extrapolate to, for example, light beams (as the one you\n> got on a laser). If there is a system in which one can fulfill the\n> condition of coherent constructive propagation is in the laser light.\n> A laser pulse has a lot more total momenta than its constitutive\n> photons (each produced by an individual atom line) however one doesnt\n> see this "total momenta wavelength" at\n> work in the physics of these systems, at least nothing\n> im aware.\n>\n> any insights about this?\n\nI think a better way to put this is to borrow from Galileo. In criticizing the\nAristotelian physics, he asked: if bodies fall at a rate proportional to their\nmass, then what would happen to two rocks tied together? Is the string\nincidental (leaving the rocks falling at their individual rates), or does it\n"count" to making the pair into a "single object?" Would it matter if we tied\nthem loosely, versus gluing the strings on, etc. The whole matter of what\nconstitutes a "single object" is revealed to be ambiguous, and suspect for\ndetermining physical properties. *However*, this is exactly the dilemma for QM!\nThink of it: if we define wavelength as per the mass "of a particle," what\nhappens in Galileo\'s case? It\'s hard to tie particles together, but why would\none "collection" (like a nucleus) behave as "an" object, and some other\nassociation (positronium?) perhaps behave as two objects, with wavelengths\naccording to what should count as "one" object? How about an atom: why can\'t the\norbiting electrons show wavelength properties relevant to the individual masses\nof electrons, as when atoms diffract through crystals, etc? I have heard some\ndiscussion of this, but was never really satisfied. What does anyone know, and\nwhat experiments have been done? What "individualization" of collections can be\nfound, under what criteria?\n\nN. Bates\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Charles J. Quarra" <disposablemailaccountfornews@yahoo.com.ar> wrote in message
news:bc979c06.0408091425.528ca2fa@posting.google.c om...
>
>
> Hi,
>
> Frequently, in introductory quantum mechanics books the relation
> between wavelength-momentum is used uncospicuously for macroscopic
> objects, probably for didactic purposes, however i see a problem with
> that extrapolation: if one would go on and adding the momenta of the
> composite objects to obtain a "body-momenta", then one should ask if
> why that cant extrapolate to, for example, light beams (as the one you
> got on a laser). If there is a system in which one can fulfill the
> condition of coherent constructive propagation is in the laser light.
> A laser pulse has a lot more total momenta than its constitutive
> photons (each produced by an individual atom line) however one doesnt
> see this "total momenta wavelength" at
> work in the physics of these systems, at least nothing
> im aware.
>
> any insights about this?
I think a better way to put this is to borrow from Galileo. In criticizing the
Aristotelian physics, he asked: if bodies fall at a rate proportional to their
mass, then what would happen to two rocks tied together? Is the string
incidental (leaving the rocks falling at their individual rates), or does it
"count" to making the pair into a "single object?" Would it matter if we tied
them loosely, versus gluing the strings on, etc. The whole matter of what
constitutes a "single object" is revealed to be ambiguous, and suspect for
determining physical properties. *However*, this is exactly the dilemma for QM!
Think of it: if we define wavelength as per the mass "of a particle," what
happens in Galileo's case? It's hard to tie particles together, but why would
one "collection" (like a nucleus) behave as "an" object, and some other
association (positronium?) perhaps behave as two objects, with wavelengths
according to what should count as "one" object? How about an atom: why can't the
orbiting electrons show wavelength properties relevant to the individual masses
of electrons, as when atoms diffract through crystals, etc? I have heard some
discussion of this, but was never really satisfied. What does anyone know, and
what experiments have been done? What "individualization" of collections can be
found, under what criteria?
N. Bates
Doug Goncz
Aug23-04, 04:05 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nDear Neil,\n\nYou ("Neil" <paradoxer@lykose.com>) wrote in message\n\nnews:<10hsucq5r51hc8b@corp.supernews.co m>...\n\n> I think a better way to put this is to borrow from Galileo. In criticizing the\n> Aristotelian physics, he asked: if bodies fall at a rate proportional to their\n> mass, then what would happen to two rocks tied together? Is the string\n> incidental (leaving the rocks falling at their individual rates), or does it\n> "count" to making the pair into a "single object?" Would it matter if we tied\n> them loosely, versus gluing the strings on, etc. The whole matter of what\n> constitutes a "single object" is revealed to be ambiguous, and suspect for\n> determining physical properties. *However*, this is exactly the dilemma for QM!\n> Think of it: if we define wavelength as per the mass "of a particle," what\n> happens in Galileo\'s case? It\'s hard to tie particles together, but why would\n> one "collection" (like a nucleus) behave as "an" object, and some other\n> association (positronium?) perhaps behave as two objects, with wavelengths\n> according to what should count as "one" object?\n\nBecause of the nature of the binding. String is fine for Galileo but\nthere are multiple inter-subatomic forces at work in "collections".\n\n> How about an atom: why can\'t the\n> orbiting electrons show wavelength properties relevant to the individual masses\n> of electrons, as when atoms diffract through crystals, etc?\n\nAren\'t these masked?\n\n> I have heard some\n> discussion of this, but was never really satisfied.\n\nWhat was missing?\n\n> What does anyone know, and\n> what experiments have been done?\n\nI do know, for sure, that particles as large as buckyballs have been\nshown to posees a wavelength characteristic. Search Google Groups for\ndgoncz and "buckybeam".\n\n> What "individualization" of collections can be\n> found, under what criteria?\n\nIndistinguishibility plays a large part. In the interaction of\ninterest, the individuals must be indistinguishible, that is, not just\nfunctionally but completely interchangeable, for certain properties to\nemerge ensemble.\n\nYours,\n\nDoug Goncz\nReplikon Research\nSeven Corners, VA 22044-0394\n\nBless me, Father, for I have smoked.\nIt has been eleven hours since my last cigarette.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Dear Neil,
You ("Neil" <paradoxer@lykose.com>) wrote in message
news:<10hsucq5r51hc8b@corp.supernews.com>...
> I think a better way to put this is to borrow from Galileo. In criticizing the
> Aristotelian physics, he asked: if bodies fall at a rate proportional to their
> mass, then what would happen to two rocks tied together? Is the string
> incidental (leaving the rocks falling at their individual rates), or does it
> "count" to making the pair into a "single object?" Would it matter if we tied
> them loosely, versus gluing the strings on, etc. The whole matter of what
> constitutes a "single object" is revealed to be ambiguous, and suspect for
> determining physical properties. *However*, this is exactly the dilemma for QM!
> Think of it: if we define wavelength as per the mass "of a particle," what
> happens in Galileo's case? It's hard to tie particles together, but why would
> one "collection" (like a nucleus) behave as "an" object, and some other
> association (positronium?) perhaps behave as two objects, with wavelengths
> according to what should count as "one" object?
Because of the nature of the binding. String is fine for Galileo but
there are multiple inter-subatomic forces at work in "collections".
> How about an atom: why can't the
> orbiting electrons show wavelength properties relevant to the individual masses
> of electrons, as when atoms diffract through crystals, etc?
Aren't these masked?
> I have heard some
> discussion of this, but was never really satisfied.
What was missing?
> What does anyone know, and
> what experiments have been done?
I do know, for sure, that particles as large as buckyballs have been
shown to posees a wavelength characteristic. Search Google Groups for
dgoncz and "buckybeam".
> What "individualization" of collections can be
> found, under what criteria?
Indistinguishibility plays a large part. In the interaction of
interest, the individuals must be indistinguishible, that is, not just
functionally but completely interchangeable, for certain properties to
emerge ensemble.
Yours,
Doug Goncz
Replikon Research
Seven Corners, VA 22044-0394
Bless me, Father, for I have smoked.
It has been eleven hours since my last cigarette.
Charles J. Quarra
Aug24-04, 04:57 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>DGoncz@aol.com (Doug Goncz) wrote in message\n\n> I do know, for sure, that particles as large as buckyballs have been\n> shown to posees a wavelength characteristic. Search Google Groups for\n> dgoncz and "buckybeam".\n\nA question: is this wavelength/k characteristic you mention in your\nposting of the order of 60*CarbonMass*MeanVelocity/planck const. or it\ndoes look more like CarbonMass*MeanVelocity/planck?\n\nI bet the correct answer to be the latter, but i may be wrong\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>DGoncz@aol.com (Doug Goncz) wrote in message
> I do know, for sure, that particles as large as buckyballs have been
> shown to posees a wavelength characteristic. Search Google Groups for
> dgoncz and "buckybeam".
A question: is this wavelength/k characteristic you mention in your
posting of the order of 60*CarbonMass*MeanVelocity/planck const. or it
does look more like CarbonMass*MeanVelocity/planck?
I bet the correct answer to be the latter, but i may be wrong
Doug Goncz
Aug26-04, 04:29 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Dear Charles,\n\ndisposablemailaccountfornews@yahoo.com .ar (Charles J. Quarra) wrote in message news:<bc979c06.0408230557.789e71a4@posting.google. com>...\n> DGoncz@aol.com (Doug Goncz) wrote in message\n>\n> > I do know, for sure, that particles as large as buckyballs have been\n> > shown to posees a wavelength characteristic. Search Google Groups for\n> > dgoncz and "buckybeam".\n>\n> A question: is this wavelength/k characteristic you mention in your\n> posting of the order of 60*CarbonMass*MeanVelocity/planck const. or it\n> does look more like CarbonMass*MeanVelocity/planck?\n>\n> I bet the correct answer to be the latter, but i may be wrong\n\nI\'m pretty sure the latter. I think it was Uncle Al here who went on\nabout it.\n\nHere\'s the aaser post in which I coined the term "buckybeams", not\n"buckybeam", as it turned out:\n\n\nMessage 1 in thread\nFrom: Bob Cain (arcane@znet.com)\nSubject: Signifigant step toward the aaser!\n\n\nNewsgroups: sci.physics\nDate: 1999/12/09\n\n\nFrom the most recent Nature.\n\n-----------------------------------------------------------------------------------------\n"Phase-coherent amplification of atomic matter waves"\n\nS. INOUYE, T. PFAU, S. GUPTA, A. P. CHIKKATUR, A. GÖRLITZ, D. E.\nPRITCHARD & W. KETTERLE\n\nAtomic matter waves, like electromagnetic waves, can be focused,\nreflected, guided and split by currently available passive\natom-optical\nelements. However, the key for many applications of electromagnetic\nwaves lies in the availability of amplifiers. These active devices\nallow\nsmall signals to be detected, and led to the development of masers and\nlasers. Although coherent atomic beams have been produced, matter wave\namplification has not been directly observed. Here we report the\nobservation of phase-coherent amplification of atomic matter waves.\nThe\nactive medium is a Bose-Einstein condensate, pumped by light that is\nfar\noff resonance. An atomic wave packet is split off the condensate by\ndiffraction from an optical standing wave, and then amplified. We\nverified the phase coherence of the amplifier by observing\ninterference\nof the output wave with a reference wave packet. This development\nprovides a new tool for atom optics and atom interferometry, and opens\nthe way to the construction of active matter-wave devices.\n-----------------------------------------------------------------------------------------\n\nCheck out:\n\nhttp://www.nature.com/server-java/Propub/nature/402641A0.abs_frameset\n\nAnybody care to address the practical applications of this?\n\n\nThanks,\n\nBob\n\n\n----------------------\n\nThe phase coherence length is given in this Nature article, I presume.\n\nYours,\n\nDoug Goncz\nReplikon Research\nSeven Corners, Va\nFighting Terrorism with Gatorade and Muffin Bars (that is, no\ngasoline)\nI love: Dona, Jeff, Mom, Neelix, Tasha, and Teri, alphabetically.\nI drive: A Lighting Cycle Dynamics Thunderbolt recumbent with 657%\nrange.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Dear Charles,
disposablemailaccountfornews@yahoo.com.ar (Charles J. Quarra) wrote in message news:<bc979c06.0408230557.789e71a4@posting.google.com>...
> DGoncz@aol.com (Doug Goncz) wrote in message
>
> > I do know, for sure, that particles as large as buckyballs have been
> > shown to posees a wavelength characteristic. Search Google Groups for
> > dgoncz and "buckybeam".
>
> A question: is this wavelength/k characteristic you mention in your
> posting of the order of 60*CarbonMass*MeanVelocity/planck const. or it
> does look more like CarbonMass*MeanVelocity/planck?
>
> I bet the correct answer to be the latter, but i may be wrong
I'm pretty sure the latter. I think it was Uncle Al here who went on
about it.
Here's the aaser post in which I coined the term "buckybeams", not
"buckybeam", as it turned out:
Message 1 in thread
From: Bob Cain (arcane@znet.com)
Subject: Signifigant step toward the aaser!
Newsgroups: sci.physics
Date: 1999/12/09
From the most recent Nature.
-----------------------------------------------------------------------------------------
"Phase-coherent amplification of atomic matter waves"
S. INOUYE, T. PFAU, S. GUPTA, A. P. CHIKKATUR, A. GÖRLITZ, D. E.
PRITCHARD & W. KETTERLE
Atomic matter waves, like electromagnetic waves, can be focused,
reflected, guided and split by currently available passive
atom-optical
elements. However, the key for many applications of electromagnetic
waves lies in the availability of amplifiers. These active devices
allow
small signals to be detected, and led to the development of masers and
lasers. Although coherent atomic beams have been produced, matter wave
amplification has not been directly observed. Here we report the
observation of phase-coherent amplification of atomic matter waves.
The
active medium is a Bose-Einstein condensate, pumped by light that is
far
off resonance. An atomic wave packet is split off the condensate by
diffraction from an optical standing wave, and then amplified. We
verified the phase coherence of the amplifier by observing
interference
of the output wave with a reference wave packet. This development
provides a new tool for atom optics and atom interferometry, and opens
the way to the construction of active matter-wave devices.
-----------------------------------------------------------------------------------------
Check out:
http://www.nature.com/server-java/Propub/nature/402641A0.abs_frameset
Anybody care to address the practical applications of this?
Thanks,
Bob
----------------------
The phase coherence length is given in this Nature article, I presume.
Yours,
Doug Goncz
Replikon Research
Seven Corners, Va
Fighting Terrorism with Gatorade and Muffin Bars (that is, no
gasoline)
I love: Dona, Jeff, Mom, Neelix, Tasha, and Teri, alphabetically.
I drive: A Lighting Cycle Dynamics Thunderbolt recumbent with 657%
range.
Charles J. Quarra
Aug27-04, 02:41 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>DGoncz@aol.com (Doug Goncz) wrote in message news:<5d8971ea.0408250034.365e538a@posting.google. com>...\n> Dear Charles,\n>\n> disposablemailaccountfornews@yahoo.com.ar (Charles J. Quarra) wrote in message news:<bc979c06.0408230557.789e71a4@posting.google. com>...\n> > A question: is this wavelength/k characteristic you mention in your\n> > posting of the order of 60*CarbonMass*MeanVelocity/planck const. or it\n> > does look more like CarbonMass*MeanVelocity/planck?\n> >\n> > I bet the correct answer to be the latter, but i may be wrong\n>\n> I\'m pretty sure the latter. I think it was Uncle Al here who went on\n> about it.\n>\n\nWell, if thats true, then my initial suspect about the total momenta\nnot being relevant at QM physics, even for QM relevant systems\n\nWhich suggests that the momenta of composite objects is not directly\nassociated with a wavelength, at least not at the fundamental level\nthat De Broglie equation is usually applied\n\nWhich would be good for people doing Double Special Relativity, since\nmacroscopic objects exceeding easily the planck wavelength wouldnt be\na problem\n\nHas anyone done the math for this?\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>DGoncz@aol.com (Doug Goncz) wrote in message news:<5d8971ea.0408250034.365e538a@posting.google.com>...
> Dear Charles,
>
> disposablemailaccountfornews@yahoo.com.ar (Charles J. Quarra) wrote in message news:<bc979c06.0408230557.789e71a4@posting.google.com>...
> > A question: is this wavelength/k characteristic you mention in your
> > posting of the order of 60*CarbonMass*MeanVelocity/planck const. or it
> > does look more like CarbonMass*MeanVelocity/planck?
> >
> > I bet the correct answer to be the latter, but i may be wrong
>
> I'm pretty sure the latter. I think it was Uncle Al here who went on
> about it.
>
Well, if thats true, then my initial suspect about the total momenta
not being relevant at QM physics, even for QM relevant systems
Which suggests that the momenta of composite objects is not directly
associated with a wavelength, at least not at the fundamental level
that De Broglie equation is usually applied
Which would be good for people doing Double Special Relativity, since
macroscopic objects exceeding easily the planck wavelength wouldnt be
a problem
Has anyone done the math for this?
Bjorn Danielsson
Aug30-04, 03:57 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\ndisposablemailaccountfornews@yahoo.com.ar (Charles J. Quarra) wrote:\n>\n> A question: is this wavelength/k characteristic you mention in your\n> posting of the order of 60*CarbonMass*MeanVelocity/planck const. or it\n> does look more like CarbonMass*MeanVelocity/planck?\n>\n> I bet the correct answer to be the latter, but i may be wrong\n\nIt\'s more like 60*CarbonMass*MeanVelocity/planck. See the data from\nthe original experiment:\n\nhttp://www.quantum.univie.ac.at/research/matterwave/c60/\n\nThe peak of the velocity distribution was 210 m/s and the wavelength\ndetected was 2.5 picometers. Plugging in a mass of 60*12 daltons and\nthe speed 210 m/s in deBroglie\'s formula gives 2.6 picometers.\n\nI have no idea why this summing of deBroglie wavenumbers isn\'t normally\nseen in laser beams. Perhaps it\'s just very difficult to detect?\n\nBut it seems it\'s not impossible: search for "biphoton" on Google.\n\nRegards,\n\n--\nBjorn Danielsson <bonus@algonet.se>\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>disposablemailaccountfornews@yahoo.com.ar (Charles J. Quarra) wrote:
>
> A question: is this wavelength/k characteristic you mention in your
> posting of the order of 60*CarbonMass*MeanVelocity/planck const. or it
> does look more like CarbonMass*MeanVelocity/planck?
>
> I bet the correct answer to be the latter, but i may be wrong
It's more like 60*CarbonMass*MeanVelocity/planck. See the data from
the original experiment:
http://www.quantum.univie.ac.at/research/matterwave/c60/
The peak of the velocity distribution was 210 m/s and the wavelength
detected was 2.5 picometers. Plugging in a mass of 60*12 daltons and
the speed 210 m/s in deBroglie's formula gives 2.6 picometers.
I have no idea why this summing of deBroglie wavenumbers isn't normally
seen in laser beams. Perhaps it's just very difficult to detect?
But it seems it's not impossible: search for "biphoton" on Google.
Regards,
--
Bjorn Danielsson <bonus@algonet.se>
Charles J. Quarra
Aug31-04, 02:41 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Bjorn Danielsson <bonus@algonet.se> wrote in message\n> It\'s more like 60*CarbonMass*MeanVelocity/planck. See the data from\n> the original experiment:\n>\n> http://www.quantum.univie.ac.at/research/matterwave/c60/\n>\n> The peak of the velocity distribution was 210 m/s and the wavelength\n> detected was 2.5 picometers. Plugging in a mass of 60*12 daltons and\n> the speed 210 m/s in deBroglie\'s formula gives 2.6 picometers.\n>\n> I have no idea why this summing of deBroglie wavenumbers isn\'t normally\n> seen in laser beams. Perhaps it\'s just very difficult to detect?\n>\n> But it seems it\'s not impossible: search for "biphoton" on Google.\n\nInteesting. Since scattering amplitudes depend on the k, you would\nexpect that high-energy reactions in accelerators would be favoured by\ncolliding even at moderate speeds, highly massive, _composite_ objects\n(such as fullerene, or a big Z ion). Aparrently the LHC is following\nthis approach. However i wonder why this approach to achieve beams\nwith extremely high energies availables for reaction has not be\npursued before\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Bjorn Danielsson <bonus@algonet.se> wrote in message
> It's more like 60*CarbonMass*MeanVelocity/planck. See the data from
> the original experiment:
>
> http://www.quantum.univie.ac.at/research/matterwave/c60/
>
> The peak of the velocity distribution was 210 m/s and the wavelength
> detected was 2.5 picometers. Plugging in a mass of 60*12 daltons and
> the speed 210 m/s in deBroglie's formula gives 2.6 picometers.
>
> I have no idea why this summing of deBroglie wavenumbers isn't normally
> seen in laser beams. Perhaps it's just very difficult to detect?
>
> But it seems it's not impossible: search for "biphoton" on Google.
Inteesting. Since scattering amplitudes depend on the k, you would
expect that high-energy reactions in accelerators would be favoured by
colliding even at moderate speeds, highly massive, _composite_ objects
(such as fullerene, or a big Z ion). Aparrently the LHC is following
this approach. However i wonder why this approach to achieve beams
with extremely high energies availables for reaction has not be
pursued before
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nBjorn Danielsson <bonus@algonet.se> writes\n>disposablemailaccountfornews@yahoo.com.ar (Charles J. Quarra) wrote:\n>>\n>> A question: is this wavelength/k characteristic you mention in your\n>> posting of the order of 60*CarbonMass*MeanVelocity/planck const. or it\n>> does look more like CarbonMass*MeanVelocity/planck?\n>>\n>> I bet the correct answer to be the latter, but i may be wrong\n>\n>It\'s more like 60*CarbonMass*MeanVelocity/planck. See the data from\n>the original experiment:\n>\n>http://www.quantum.univie.ac.at/research/matterwave/c60/\n\nI am seriously relieved. It would batter my mental model if it was not\nso. The idea of the individual carbon atoms diffracting away differently\nto the bound group brings all sorts of complications for other systems.\nThe smaller constituents would be found a long way away, which makes no\nsense.\n\nThat said, though, the binding of the fullerene is dominated by the\ndiffraction pattern of the electrons in its outer shells (ie orbitals).\nSo the diffraction/wavefunction of the individual constituents has a\nvery significant bearing of the internal structure, that is at shorter\nranges, as one might hope for.\n\nMy problem is that as far as I know nobody has a model that takes the\nwavefunction of two particles, binds them, and then shows that at medium\ndistance the wavefunction of the pair is that of a single particle with\nthe mass of the composite. I find this extraordinary because its hugely\nbasic and something QM should be able to explain readily. That it cannot\nimplies strongly to me that there is an inherent flaw or omission in the\nmathematical construction. However nobody seems to care. Some must have\nbigger carpets than I have.\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Bjorn Danielsson <bonus@algonet.se> writes
>disposablemailaccountfornews@yahoo.com.ar (Charles J. Quarra) wrote:
>>
>> A question: is this wavelength/k characteristic you mention in your
>> posting of the order of 60*CarbonMass*MeanVelocity/planck const. or it
>> does look more like CarbonMass*MeanVelocity/planck?
>>
>> I bet the correct answer to be the latter, but i may be wrong
>
>It's more like 60*CarbonMass*MeanVelocity/planck. See the data from
>the original experiment:
>
>http://www.quantum.univie.ac.at/research/matterwave/c60/
I am seriously relieved. It would batter my mental model if it was not
so. The idea of the individual carbon atoms diffracting away differently
to the bound group brings all sorts of complications for other systems.
The smaller constituents would be found a long way away, which makes no
sense.
That said, though, the binding of the fullerene is dominated by the
diffraction pattern of the electrons in its outer shells (ie orbitals).
So the diffraction/wavefunction of the individual constituents has a
very significant bearing of the internal structure, that is at shorter
ranges, as one might hope for.
My problem is that as far as I know nobody has a model that takes the
wavefunction of two particles, binds them, and then shows that at medium
distance the wavefunction of the pair is that of a single particle with
the mass of the composite. I find this extraordinary because its hugely
basic and something QM should be able to explain readily. That it cannot
implies strongly to me that there is an inherent flaw or omission in the
mathematical construction. However nobody seems to care. Some must have
bigger carpets than I have.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
Maurice Barnhill
Sep7-04, 02:10 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Oz wrote:\n> ...\n> My problem is that as far as I know nobody has a model that takes the\n> wavefunction of two particles, binds them, and then shows that at medium\n> distance the wavefunction of the pair is that of a single particle with\n> the mass of the composite. ...\n>\nSure there is. Take the Schroedinger Equation for two particles\nat x1 and x2. Change variables to X=(m1 x1 + m2 x2)/(m1 + m2) and\nx=x1 - x2. The result is an equation involving the potential\nV(X,x) which typically doesn\'t depend on X because of overall\ntranslational invariance, and a kinetic energy of P^2/M + p^2/m,\nwhere M is the total mass, m is the reduced mass, P is the CM\nmomentum, and p is the internal momentum. If the potential (other\nthan terms representing the slit) is really independent of X, the\nsolution of this equation is the product of a plane wave in X and\na function of x, so a slit diffracts the CM wave function (in X)\nand to a good approximation at medium distances leaves the\ninternal wave function unchanged. No doubt this is more\ncomplicated in relativistic terms, much less in field theory. I\ndon\'t recall actually doing it in either case, but in principle\nit should work at least approximately. Do you know of a reason\nwhy this program does not work to adequate approximation?\n\n--\nMaurice Barnhill\nmvb@udel.edu [Use ReplyTo, not From]\n[bellatlantic.net is reserved for spam only]\nDepartment of Physics and Astronomy\nUniversity of Delaware\nNewark, DE 19716\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Oz wrote:
> ...
> My problem is that as far as I know nobody has a model that takes the
> wavefunction of two particles, binds them, and then shows that at medium
> distance the wavefunction of the pair is that of a single particle with
> the mass of the composite. ...
>
Sure there is. Take the Schroedinger Equation for two particles
at x1 and x2. Change variables to X=(m1 x1 + m2 x2)/(m1 + m2) and
x=x1 - x2. The result is an equation involving the potential
V(X,x) which typically doesn't depend on X because of overall
translational invariance, and a kinetic energy of P^2/M + p^2/m,
where M is the total mass, m is the reduced mass, P is the CM
momentum, and p is the internal momentum. If the potential (other
than terms representing the slit) is really independent of X, the
solution of this equation is the product of a plane wave in X and
a function of x, so a slit diffracts the CM wave function (in X)
and to a good approximation at medium distances leaves the
internal wave function unchanged. No doubt this is more
complicated in relativistic terms, much less in field theory. I
don't recall actually doing it in either case, but in principle
it should work at least approximately. Do you know of a reason
why this program does not work to adequate approximation?
--
Maurice Barnhill
mvb@udel.edu [Use ReplyTo, not From]
[bellatlantic.net is reserved for spam only]
Department of Physics and Astronomy
University of Delaware
Newark, DE 19716
Frank Hellmann
Sep9-04, 03:04 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Neil" <paradoxer@lykose.com> wrote in message news:<10hsucq5r51hc8b@corp.supernews.com>...\n> "Charles J. Quarra" <disposablemailaccountfornews@yahoo.com.ar> wrote in message\n> news:bc979c06.0408091425.528ca2fa@posting.google.c om...\n> The whole matter of what\n> constitutes a "single object" is revealed to be ambiguous, and suspect for\n> determining physical properties.\n\nThis ambiguity is of course solved by the elementary theorem in\nNewtonian mechanics that the center of mass of a system behaves as an\nelementary particle under external forces.\nThis renders the conceptual basis of newtonian mechanics, the\napproximation of masses as point particles, consistent with the\ntheory. Things become more difficult in SR and especially GR, and the\nconceptual basis has to be refined quite a bit, but it still works.\nSomething like this qould be great for QM I would suspect it would be\n(at least slightly) more subtle then Newtonian Mechanics though...\nWhen i asked whether such a thing exists here on SPR a while ago I was\ntold that you could simply quantize the compsit system and would get\nthe result. That is of course unsatisfactory, since we want to work\nentirely in the context of QM to be able to anwser exactl this kind of\nquestions: How do the internal degrees of freedom get masked, and how\ndo they lump together to create a "center of mass" wave function.\nSince ordinary QM obeys the Galileo group I guess one should try\ntransforming a system into the appropriate coordinates and see if one\nget\'s something out of this.\nShould be a nice little problem (hardly original) for somebody with\nsome time on their hands...\n\n---\nfrank\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Neil" <paradoxer@lykose.com> wrote in message news:<10hsucq5r51hc8b@corp.supernews.com>...
> "Charles J. Quarra" <disposablemailaccountfornews@yahoo.com.ar> wrote in message
> news:bc979c06.0408091425.528ca2fa@posting.google.c om...
> The whole matter of what
> constitutes a "single object" is revealed to be ambiguous, and suspect for
> determining physical properties.
This ambiguity is of course solved by the elementary theorem in
Newtonian mechanics that the center of mass of a system behaves as an
elementary particle under external forces.
This renders the conceptual basis of newtonian mechanics, the
approximation of masses as point particles, consistent with the
theory. Things become more difficult in SR and especially GR, and the
conceptual basis has to be refined quite a bit, but it still works.
Something like this qould be great for QM I would suspect it would be
(at least slightly) more subtle then Newtonian Mechanics though...
When i asked whether such a thing exists here on SPR a while ago I was
told that you could simply quantize the compsit system and would get
the result. That is of course unsatisfactory, since we want to work
entirely in the context of QM to be able to anwser exactl this kind of
questions: How do the internal degrees of freedom get masked, and how
do they lump together to create a "center of mass" wave function.
Since ordinary QM obeys the Galileo group I guess one should try
transforming a system into the appropriate coordinates and see if one
get's something out of this.
Should be a nice little problem (hardly original) for somebody with
some time on their hands...
---
frank
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nFrank Hellmann <Certhas@gmail.com> writes\n>told that you could simply quantize the compsit system and would get\n>the result. That is of course unsatisfactory, since we want to work\n>entirely in the context of QM to be able to anwser exactl this kind of\n>questions: How do the internal degrees of freedom get masked, and how\n>do they lump together to create a "center of mass" wave function.\n\nAn alternative using schroedinger has been proposed on this thread, but\nI am not sure of its implied assumptions.\n\nTaking an intuitive stance (about all I am fit to do) I think the key is\nthat the system is *bound*. That is the wavefunction of the composite is\nnot the same as that of the individual components.\n\nFor an atom we accept without thinking that the wavefunction of the\nelectron in a H atom is not remotely the same as that of a free\nelectron. It\'s in a potential well and so has quite a different form.\n\nAlthough I\'ve never seen it cited anywhere I would expect the\nwavefunction of the nucleus would also be different to that of an\nisolated proton. The wavefunction of the composite would be some\ncombination of these.\n\nOn reflection, then, its obvious that the wavefunction of a bunch of\ngravitationally bound particles will be different to that of each of\nthem individually. For one thing it won\'t extend \'far from the centre of\nmass\' (for some value of \'far\'). The implication is thus then that an\nensemble will have a wavefunction that comprises, in some sense, a\ncontribution from all the particles it is bound to. For small\nelectrically bound particles like fullerenes, where the binding is very\nstrong indeed, it would be expected to find a composite description. You\nsimply have a very low probability of diffraction one electron (even)\ndifferently to the rest - the binding sees to that. Basically you can\'t\ndiffract a single electron away without diffracting the rest of the\nparticle.\n\nI think there should be a corollary to this though. That is that the\nwavefunctions of the individual particles must have a wavelength in\ncommon at some level. That is, the effect of binding must synchronise\ntheir wavefunctions. Why it should be the sum, rather than the\ndifference is a tad unclear to me right now.\n\nChris Hillman (I think) once gave an intriguing rational of the force of\ngravity just using time changes and QM, that I had saved for years but\nis now lost. Although we are not talking about just gravity here, I have\na mostly forgotten memory that his \'mechanism\' would be useful here.\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Frank Hellmann <Certhas@gmail.com> writes
>told that you could simply quantize the compsit system and would get
>the result. That is of course unsatisfactory, since we want to work
>entirely in the context of QM to be able to anwser exactl this kind of
>questions: How do the internal degrees of freedom get masked, and how
>do they lump together to create a "center of mass" wave function.
An alternative using schroedinger has been proposed on this thread, but
I am not sure of its implied assumptions.
Taking an intuitive stance (about all I am fit to do) I think the key is
that the system is *bound*. That is the wavefunction of the composite is
not the same as that of the individual components.
For an atom we accept without thinking that the wavefunction of the
electron in a H atom is not remotely the same as that of a free
electron. It's in a potential well and so has quite a different form.
Although I've never seen it cited anywhere I would expect the
wavefunction of the nucleus would also be different to that of an
isolated proton. The wavefunction of the composite would be some
combination of these.
On reflection, then, its obvious that the wavefunction of a bunch of
gravitationally bound particles will be different to that of each of
them individually. For one thing it won't extend 'far from the centre of
mass' (for some value of 'far'). The implication is thus then that an
ensemble will have a wavefunction that comprises, in some sense, a
contribution from all the particles it is bound to. For small
electrically bound particles like fullerenes, where the binding is very
strong indeed, it would be expected to find a composite description. You
simply have a very low probability of diffraction one electron (even)
differently to the rest - the binding sees to that. Basically you can't
diffract a single electron away without diffracting the rest of the
particle.
I think there should be a corollary to this though. That is that the
wavefunctions of the individual particles must have a wavelength in
common at some level. That is, the effect of binding must synchronise
their wavefunctions. Why it should be the sum, rather than the
difference is a tad unclear to me right now.
Chris Hillman (I think) once gave an intriguing rational of the force of
gravity just using time changes and QM, that I had saved for years but
is now lost. Although we are not talking about just gravity here, I have
a mostly forgotten memory that his 'mechanism' would be useful here.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
p.kinsler@imperial.ac.uk
Sep16-04, 07:09 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nCharles J. Quarra <disposablemailaccountfornews@yahoo.com.ar> wrote:\n> well, of course. Let me rephrase a little better what i said; a laser\n> pulse has a _total momenta_ a lot bigger than the individual momenta\n> of any of its constitutive photons, however one doesnt see this "total\n> momenta wavelength" at work in the physics of these systems (i.e:\n> lasers) at least nothing im aware of.\n\nThis post deserves an answer, and I\'m going to try to give one,\nbut for reasons of time I\'m going to have to resort to a bit\nof handwaving to get across the flavour of what I think is\nthe answer.\n\nWhen getting a "total momenta wavelength" for a macroscopic body,\nyou are rexpressing the simple many-body wavefunction (perhaps\njust a product of all the individual single body wavefunctions)\nin a new way -- with one centre-of-mass (COM) wavefunction and then\nthe remaining difference-like parts multipled on. This COM\nwavefunction is naturally like the product of N functions\nwiggling away with momentum P, hence the COM wavefunction wiggles\nin space according to NP.\n\nFor a laser pulse it\'s different. It\'s the field modes that carry\nthe information about photon momentum, not the wavefunctions.\nThe wavefunction(s) of the photons live inside the field modes. If\nyou\'ve got N photons inside a single field mode, the photon wavefunction\nhas N-like wiggles, but this has nothing to do with the spatial\nwiggling of the field mode due to its momentum P. When working out\nmomentum related stuff to do with this laser pulse, you get a P\nfrom the field mode and an N from the wavefunction of the photons.\n\n\n--\n---------------------------------+---------------------------------\nDr. Paul Kinsler\nBlackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714\nImperial College London, Dr.Paul.Kinsler@physics.org\nSW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Charles J. Quarra <disposablemailaccountfornews@yahoo.com.ar> wrote:
> well, of course. Let me rephrase a little better what i said; a laser
> pulse has a _total momenta_ a lot bigger than the individual momenta
> of any of its constitutive photons, however one doesnt see this "total
> momenta wavelength" at work in the physics of these systems (i.e:
> lasers) at least nothing im aware of.
This post deserves an answer, and I'm going to try to give one,
but for reasons of time I'm going to have to resort to a bit
of handwaving to get across the flavour of what I think is
the answer.
When getting a "total momenta wavelength" for a macroscopic body,
you are rexpressing the simple many-body wavefunction (perhaps
just a product of all the individual single body wavefunctions)
in a new way -- with one centre-of-mass (COM) wavefunction and then
the remaining difference-like parts multipled on. This COM
wavefunction is naturally like the product of N functions
wiggling away with momentum P, hence the COM wavefunction wiggles
in space according to NP.
For a laser pulse it's different. It's the field modes that carry
the information about photon momentum, not the wavefunctions.
The wavefunction(s) of the photons live inside the field modes. If
you've got N photons inside a single field mode, the photon wavefunction
has N-like wiggles, but this has nothing to do with the spatial
wiggling of the field mode due to its momentum P. When working out
momentum related stuff to do with this laser pulse, you get a P
from the field mode and an N from the wavefunction of the photons.
--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\np.kinsler@imperial.ac.uk writes\n>When getting a "total momenta wavelength" for a macroscopic body,\n>you are rexpressing the simple many-body wavefunction (perhaps\n>just a product of all the individual single body wavefunctions)\n>in a new way -- with one centre-of-mass (COM) wavefunction and then\n>the remaining difference-like parts multipled on.\n\nI accept this is what happens. Although another poster suggested a\nmethod I will admit to not following the argument. However that\'s not\nwhat I want to discuss here.\n\n>This COM\n>wavefunction is naturally like the product of N functions\n>wiggling away with momentum P, hence the COM wavefunction wiggles\n>in space according to NP.\n\nOK, given the above.\n\n>For a laser pulse it\'s different. It\'s the field modes that carry\n>the information about photon momentum, not the wavefunctions.\n>The wavefunction(s) of the photons live inside the field modes. If\n>you\'ve got N photons inside a single field mode, the photon wavefunction\n>has N-like wiggles, but this has nothing to do with the spatial\n>wiggling of the field mode due to its momentum P. When working out\n>momentum related stuff to do with this laser pulse, you get a P\n>from the field mode and an N from the wavefunction of the photons.\n\nI accept this is what happens. I am looking for a rationale.\n\nIs it because the difference between the two examples is that one (the\nfirst) is a bound system (\'a compound\') whilst the second is unbound.\nThat is each photon is doing its thing independently of the others\n(ignoring any effects of the emitter) so (in effect) we just add\namplitude (N) to the field (P). Removing one or more photons has no\neffect on the rest, and its easy and energy cheap (if not free) for\nexample by using a half-silvered mirror.\n\nThe bound system is inherently different. Ignoring gravity for a bunch\nof reasonable reasons, they are typically strongly bound by electric\nfields. In effect (er and actually) sitting inside a mutual potential\nwell. Now, when you think about it diffraction occurs only (I can\'t\nthink of a counter-example) to beams of independent particles (like your\nphotons above). That is its energetically cheap to do diffraction, and\nif you consider the average change in momentum its free. To diffract\n*part* of a bound system is most definitely not energy-free.\n\nFor any one constituent of the bound system one would naively expect to\nsuperimpose the (very low) probability of finding it far from \'the rest\nof the compound\' onto the diffraction pattern. This will effectively\nquickly attenuate any constituent\'s pattern to zero in the typical\nexample.\n\nI\'d be surprised if this wasn\'t a strong argument that better people\nthan me could prove mathematically.\n\nThis doesn\'t, though, really give me an argument for why a compound\nshould behave like an elementary particle with momentum of the sum of\nits constituent parts. It might, though, give a clue. If I can get my\nhead round it.\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>p.kinsler@imperial.ac.uk writes
>When getting a "total momenta wavelength" for a macroscopic body,
>you are rexpressing the simple many-body wavefunction (perhaps
>just a product of all the individual single body wavefunctions)
>in a new way -- with one centre-of-mass (COM) wavefunction and then
>the remaining difference-like parts multipled on.
I accept this is what happens. Although another poster suggested a
method I will admit to not following the argument. However that's not
what I want to discuss here.
>This COM
>wavefunction is naturally like the product of N functions
>wiggling away with momentum P, hence the COM wavefunction wiggles
>in space according to NP.
OK, given the above.
>For a laser pulse it's different. It's the field modes that carry
>the information about photon momentum, not the wavefunctions.
>The wavefunction(s) of the photons live inside the field modes. If
>you've got N photons inside a single field mode, the photon wavefunction
>has N-like wiggles, but this has nothing to do with the spatial
>wiggling of the field mode due to its momentum P. When working out
>momentum related stuff to do with this laser pulse, you get a P
>from the field mode and an N from the wavefunction of the photons.
I accept this is what happens. I am looking for a rationale.
Is it because the difference between the two examples is that one (the
first) is a bound system ('a compound') whilst the second is unbound.
That is each photon is doing its thing independently of the others
(ignoring any effects of the emitter) so (in effect) we just add
amplitude (N) to the field (P). Removing one or more photons has no
effect on the rest, and its easy and energy cheap (if not free) for
example by using a half-silvered mirror.
The bound system is inherently different. Ignoring gravity for a bunch
of reasonable reasons, they are typically strongly bound by electric
fields. In effect (er and actually) sitting inside a mutual potential
well. Now, when you think about it diffraction occurs only (I can't
think of a counter-example) to beams of independent particles (like your
photons above). That is its energetically cheap to do diffraction, and
if you consider the average change in momentum its free. To diffract
*part* of a bound system is most definitely not energy-free.
For any one constituent of the bound system one would naively expect to
superimpose the (very low) probability of finding it far from 'the rest
of the compound' onto the diffraction pattern. This will effectively
quickly attenuate any constituent's pattern to zero in the typical
example.
I'd be surprised if this wasn't a strong argument that better people
than me could prove mathematically.
This doesn't, though, really give me an argument for why a compound
should behave like an elementary particle with momentum of the sum of
its constituent parts. It might, though, give a clue. If I can get my
head round it.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
Maurice Barnhill
Sep19-04, 10:38 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nOz wrote:\n> p.kinsler@imperial.ac.uk writes\n>\n>>When getting a "total momenta wavelength" for a macroscopic body,\n>>you are rexpressing the simple many-body wavefunction (perhaps\n>>just a product of all the individual single body wavefunctions)\n>>in a new way -- with one centre-of-mass (COM) wavefunction and then\n>>the remaining difference-like parts multipled on.\n>\n>\n> I accept this is what happens. Although another poster suggested a\n> method I will admit to not following the argument. However that\'s not\n> what I want to discuss here.\n>\n\nThe two suggestions are the same. The fact that the wave\nfunction is a product of a CM wavefunction and internal\n"difference-like" wavefunctions is found by solving the\nSchroedinger Equation in the way I suggested elsewhere. You can\nthink of the process whichever way is easier to follow. If you\naccept the non-relativistic Schroedinger Equation as the proper\ndescription of the system, this form of the wave-function follows\nmathematically. You cannot escape it.\n>\n[snip]\n--\nMaurice Barnhill\nmvb@udel.edu [Use ReplyTo, not From]\n[bellatlantic.net is reserved for spam only]\nDepartment of Physics and Astronomy\nUniversity of Delaware\nNewark, DE 19716\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Oz wrote:
> p.kinsler@imperial.ac.uk writes
>
>>When getting a "total momenta wavelength" for a macroscopic body,
>>you are rexpressing the simple many-body wavefunction (perhaps
>>just a product of all the individual single body wavefunctions)
>>in a new way -- with one centre-of-mass (COM) wavefunction and then
>>the remaining difference-like parts multipled on.
>
>
> I accept this is what happens. Although another poster suggested a
> method I will admit to not following the argument. However that's not
> what I want to discuss here.
>
The two suggestions are the same. The fact that the wave
function is a product of a CM wavefunction and internal
"difference-like" wavefunctions is found by solving the
Schroedinger Equation in the way I suggested elsewhere. You can
think of the process whichever way is easier to follow. If you
accept the non-relativistic Schroedinger Equation as the proper
description of the system, this form of the wave-function follows
mathematically. You cannot escape it.
>
[snip]
--
Maurice Barnhill
mvb@udel.edu [Use ReplyTo, not From]
[bellatlantic.net is reserved for spam only]
Department of Physics and Astronomy
University of Delaware
Newark, DE 19716
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nMaurice Barnhill <mvb@udel.edu> writes\n\n>Take the Schroedinger Equation for two particles\n>at x1 and x2. Change variables to X=(m1 x1 + m2 x2)/(m1 + m2) and\n>x=x1 - x2.\n\nOk variables changed to centre of mass.\nThis is going to result in some messy math, I think.\n\n>The result is an equation involving the potential\n>V(X,x)\n\nOk. Might be a tad ugh!\n\n>which typically doesn\'t depend on X because of overall\n>translational invariance,\n\nI\'m not wholly convinced of this unless, perhaps, you are taking it to\nfirst order.\n\n>and a kinetic energy of P^2/M + p^2/m,\n>where M is the total mass, m is the reduced mass, P is the CM\n>momentum, and p is the internal momentum.\n\nI\'ll believe you.\n\n>If the potential (other\n>than terms representing the slit) is really independent of X, the\n>solution of this equation is the product of a plane wave in X and\n>a function of x, so a slit diffracts the CM wave function (in X)\n>and to a good approximation at medium distances leaves the\n>internal wave function unchanged.\n\nOK. I accept what you are saying.\nI didn\'t dispute the result, I just had never come across an actual\nanalysis.\n\n>No doubt this is more\n>complicated in relativistic terms, much less in field theory. I\n>don\'t recall actually doing it in either case, but in principle\n>it should work at least approximately. Do you know of a reason\n>why this program does not work to adequate approximation?\n\nMe? Noooo (aghast at the thought).\n\nNB To some extent at least, and I can\'t see why the mechanics should not\nbe the same, this should apply even to free unbound particles. Thus one\nshould get some short wavelength effects from diffracting a collimated\nbunch of, say, neutrons. In reality though, the effect would be very\nsmall.\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Maurice Barnhill <mvb@udel.edu> writes
>Take the Schroedinger Equation for two particles
>at x1 and x2. Change variables to X=(m1 x1 + m2 x2)/(m1 + m2) and
>x=x1 - x2.
Ok variables changed to centre of mass.
This is going to result in some messy math, I think.
>The result is an equation involving the potential
>V(X,x)
Ok. Might be a tad ugh!
>which typically doesn't depend on X because of overall
>translational invariance,
I'm not wholly convinced of this unless, perhaps, you are taking it to
first order.
>and a kinetic energy of P^2/M + p^2/m,
>where M is the total mass, m is the reduced mass, P is the CM
>momentum, and p is the internal momentum.
I'll believe you.
>If the potential (other
>than terms representing the slit) is really independent of X, the
>solution of this equation is the product of a plane wave in X and
>a function of x, so a slit diffracts the CM wave function (in X)
>and to a good approximation at medium distances leaves the
>internal wave function unchanged.
OK. I accept what you are saying.
I didn't dispute the result, I just had never come across an actual
analysis.
>No doubt this is more
>complicated in relativistic terms, much less in field theory. I
>don't recall actually doing it in either case, but in principle
>it should work at least approximately. Do you know of a reason
>why this program does not work to adequate approximation?
Me? Noooo (aghast at the thought).
NB To some extent at least, and I can't see why the mechanics should not
be the same, this should apply even to free unbound particles. Thus one
should get some short wavelength effects from diffracting a collimated
bunch of, say, neutrons. In reality though, the effect would be very
small.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nMaurice Barnhill <mvb@udel.edu> writes\n>\n>Oz wrote:\n>>\n>> I accept this is what happens. Although another poster suggested a\n>> method I will admit to not following the argument. However that\'s not\n>> what I want to discuss here.\n>>\n>\n>The two suggestions are the same. The fact that the wave\n>function is a product of a CM wavefunction and internal\n>"difference-like" wavefunctions is found by solving the\n>Schroedinger Equation in the way I suggested elsewhere.\n\nOnce I might have been able to do this. It must surely be two particles\neach being a potential well for the other. Hmm, actually you could\napproximate this at some distance to make it one (composite) particle in\na potential well. OK, I see how it works now, I\'m pretty sure.\n\nIts easier to see if you consider two equal sized massive particles of\n(say) opposite charge (but for long life not antiparticles). Each one is\nindividually bound inside a potential well so from a long distance they\nought to look like a single particle. So effective binding is a\nnecessity.\n\nOne can then extend this to unbound particles.\n\nI may try an unravel your original post.\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Maurice Barnhill <mvb@udel.edu> writes
>
>Oz wrote:
>>
>> I accept this is what happens. Although another poster suggested a
>> method I will admit to not following the argument. However that's not
>> what I want to discuss here.
>>
>
>The two suggestions are the same. The fact that the wave
>function is a product of a CM wavefunction and internal
>"difference-like" wavefunctions is found by solving the
>Schroedinger Equation in the way I suggested elsewhere.
Once I might have been able to do this. It must surely be two particles
each being a potential well for the other. Hmm, actually you could
approximate this at some distance to make it one (composite) particle in
a potential well. OK, I see how it works now, I'm pretty sure.
Its easier to see if you consider two equal sized massive particles of
(say) opposite charge (but for long life not antiparticles). Each one is
individually bound inside a potential well so from a long distance they
ought to look like a single particle. So effective binding is a
necessity.
One can then extend this to unbound particles.
I may try an unravel your original post.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
Maurice Barnhill
Sep21-04, 03:30 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nOz wrote:\n> Maurice Barnhill <mvb@udel.edu> writes\n>\n>\n>>Take the Schroedinger Equation for two particles\n>>at x1 and x2. Change variables to X=(m1 x1 + m2 x2)/(m1 + m2) and\n>>x=x1 - x2.\n>\n>\n> Ok variables changed to centre of mass.\n> This is going to result in some messy math, I think.\n>\nNot as bad as you might think, except possibly for the potential\n>\n>>The result is an equation involving the potential\n>>V(X,x)\n>\n>\n> Ok. Might be a tad ugh!\n\nYes it can be. However, for thinking about slits, we are letting\nthe bound system travel around with no net force applied, and in\nthis case V(X,x)= function of x only.\n>\n>\n>>which typically doesn\'t depend on X because of overall\n>>translational invariance,\n>\n>\n> I\'m not wholly convinced of this unless, perhaps, you are taking it to\n> first order.\n>\n>\n\nWell I am sweeping a little bit under the rug. I want to do the\ntransformation to center of mass variables first, and add the\npotential representing the slit later. The slit involves X only\nto lowest order in the assumption that the size of the bound\nstate is small compared to the width of the slit. That\'s fair\nfor what we are trying to do.\n\n>>and a kinetic energy of P^2/M + p^2/m,\n>>where M is the total mass, m is the reduced mass, P is the CM\n>>momentum, and p is the internal momentum.\n>\n>\n> I\'ll believe you.\n>\n>\n>>If the potential (other\n>>than terms representing the slit) is really independent of X, the\n>>solution of this equation is the product of a plane wave in X and\n>>a function of x, so a slit diffracts the CM wave function (in X)\n>>and to a good approximation at medium distances leaves the\n>>internal wave function unchanged.\n>\n>\n> OK. I accept what you are saying.\n> I didn\'t dispute the result, I just had never come across an actual\n> analysis.\n>\n>\n>>No doubt this is more\n>>complicated in relativistic terms, much less in field theory. I\n>>don\'t recall actually doing it in either case, but in principle\n>>it should work at least approximately. Do you know of a reason\n>>why this program does not work to adequate approximation?\n>\n>\n> Me? Noooo (aghast at the thought).\n>\n> NB To some extent at least, and I can\'t see why the mechanics should not\n> be the same, this should apply even to free unbound particles. Thus one\n> should get some short wavelength effects from diffracting a collimated\n> bunch of, say, neutrons. In reality though, the effect would be very\n> small.\n>\nThe analysis indeed applies to the unbound case as well, except\nthere is a catch. The potential V(x) is now zero since there is\nno binding, the internal state is exp(ikx) for any k you wish,\nand the size of the internal state is infinite. The\napproximation that the size of the bound state is small compared\nto the size of the slit fails miserably.\n\nYou can arrange combinations of plane waves to make a wave packet\nthat keeps the two particles close enough together for long\nenough that the analysis is likely to work. There was a mention\nof a laser pulse elsewhere in this thread, and you could use\ncenter-of-mass variables on an unbound state to understand that\nproblem. I am not sure that the math would be non-messy, but it\nmight be fun to try it.\n\n--\nMaurice Barnhill\nmvb@udel.edu [Use ReplyTo, not From]\n[bellatlantic.net is reserved for spam only]\nDepartment of Physics and Astronomy\nUniversity of Delaware\nNewark, DE 19716\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Oz wrote:
> Maurice Barnhill <mvb@udel.edu> writes
>
>
>>Take the Schroedinger Equation for two particles
>>at x1 and x2. Change variables to X=(m1 x1 + m2 x2)/(m1 + m2) and
>>x=x1 - x2.
>
>
> Ok variables changed to centre of mass.
> This is going to result in some messy math, I think.
>
Not as bad as you might think, except possibly for the potential
>
>>The result is an equation involving the potential
>>V(X,x)
>
>
> Ok. Might be a tad ugh!
Yes it can be. However, for thinking about slits, we are letting
the bound system travel around with no net force applied, and in
this case V(X,x)= function of x only.
>
>
>>which typically doesn't depend on X because of overall
>>translational invariance,
>
>
> I'm not wholly convinced of this unless, perhaps, you are taking it to
> first order.
>
>
Well I am sweeping a little bit under the rug. I want to do the
transformation to center of mass variables first, and add the
potential representing the slit later. The slit involves X only
to lowest order in the assumption that the size of the bound
state is small compared to the width of the slit. That's fair
for what we are trying to do.
>>and a kinetic energy of P^2/M + p^2/m,
>>where M is the total mass, m is the reduced mass, P is the CM
>>momentum, and p is the internal momentum.
>
>
> I'll believe you.
>
>
>>If the potential (other
>>than terms representing the slit) is really independent of X, the
>>solution of this equation is the product of a plane wave in X and
>>a function of x, so a slit diffracts the CM wave function (in X)
>>and to a good approximation at medium distances leaves the
>>internal wave function unchanged.
>
>
> OK. I accept what you are saying.
> I didn't dispute the result, I just had never come across an actual
> analysis.
>
>
>>No doubt this is more
>>complicated in relativistic terms, much less in field theory. I
>>don't recall actually doing it in either case, but in principle
>>it should work at least approximately. Do you know of a reason
>>why this program does not work to adequate approximation?
>
>
> Me? Noooo (aghast at the thought).
>
> NB To some extent at least, and I can't see why the mechanics should not
> be the same, this should apply even to free unbound particles. Thus one
> should get some short wavelength effects from diffracting a collimated
> bunch of, say, neutrons. In reality though, the effect would be very
> small.
>
The analysis indeed applies to the unbound case as well, except
there is a catch. The potential V(x) is now zero since there is
no binding, the internal state is \exp(ikx) for any k you wish,
and the size of the internal state is infinite. The
approximation that the size of the bound state is small compared
to the size of the slit fails miserably.
You can arrange combinations of plane waves to make a wave packet
that keeps the two particles close enough together for long
enough that the analysis is likely to work. There was a mention
of a laser pulse elsewhere in this thread, and you could use
center-of-mass variables on an unbound state to understand that
problem. I am not sure that the math would be non-messy, but it
might be fun to try it.
--
Maurice Barnhill
mvb@udel.edu [Use ReplyTo, not From]
[bellatlantic.net is reserved for spam only]
Department of Physics and Astronomy
University of Delaware
Newark, DE 19716
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Maurice Barnhill <mvb@udel.edu> writes\n\n>The analysis indeed applies to the unbound case as well, except\n>there is a catch. The potential V(x) is now zero since there is\n>no binding, the internal state is exp(ikx) for any k you wish,\n>and the size of the internal state is infinite. The\n>approximation that the size of the bound state is small compared\n>to the size of the slit fails miserably.\n\nTrue. I was thinking about gravity here, but it is dreadfully weak.\n\n>You can arrange combinations of plane waves to make a wave packet\n>that keeps the two particles close enough together for long\n>enough that the analysis is likely to work. There was a mention\n>of a laser pulse elsewhere in this thread, and you could use\n>center-of-mass variables on an unbound state to understand that\n>problem.\n\nIt should be possible to have quite dense bunches of neutrons (which is\nwhy I used it for my example), but the problem would be that they have a\nnasty tendency to fall out of the apparatus if they are too cold.\n\n>I am not sure that the math would be non-messy, but it\n>might be fun to try it.\n\n<eek!>\n\n<cough>\n\n<brightly>\n\nMaybe someone has already done it?\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Maurice Barnhill <mvb@udel.edu> writes
>The analysis indeed applies to the unbound case as well, except
>there is a catch. The potential V(x) is now zero since there is
>no binding, the internal state is \exp(ikx) for any k you wish,
>and the size of the internal state is infinite. The
>approximation that the size of the bound state is small compared
>to the size of the slit fails miserably.
True. I was thinking about gravity here, but it is dreadfully weak.
>You can arrange combinations of plane waves to make a wave packet
>that keeps the two particles close enough together for long
>enough that the analysis is likely to work. There was a mention
>of a laser pulse elsewhere in this thread, and you could use
>center-of-mass variables on an unbound state to understand that
>problem.
It should be possible to have quite dense bunches of neutrons (which is
why I used it for my example), but the problem would be that they have a
nasty tendency to fall out of the apparatus if they are too cold.
>I am not sure that the math would be non-messy, but it
>might be fun to try it.
<eek!>
<cough>
<brightly>
Maybe someone has already done it?
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
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