View Full Version : Stern-Gerlach Experiment2
<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 Members,\n\nIn Late Sakurai\'s " Modern Quantum Mechanics", in the description of\nStern-Gerlach experiment, you read "Because the atom as a whole is very\nHEAVY, we expect that the CLASSICAL CONCEPT of trajectory can be\nlegitimately applied, ... " (p.3) what is the relevance of "heaviness\nof atom" to classical concept of trajectory?\nregards,\n\nAli\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 Members,
In Late Sakurai's " Modern Quantum Mechanics", in the description of
Stern-Gerlach experiment, you read "Because the atom as a whole is very
HEAVY, we expect that the CLASSICAL CONCEPT of trajectory can be
legitimately applied, ... " (p.3) what is the relevance of "heaviness
of atom" to classical concept of trajectory?
regards,
Ali
Igor Khavkine
May29-05, 01:26 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>On 2005-05-28, Ali <ph_question@yahoo.com> wrote:\n> Dear Members,\n>\n> In Late Sakurai\'s " Modern Quantum Mechanics", in the description of\n> Stern-Gerlach experiment, you read "Because the atom as a whole is very\n> HEAVY, we expect that the CLASSICAL CONCEPT of trajectory can be\n> legitimately applied, ... " (p.3) what is the relevance of "heaviness\n> of atom" to classical concept of trajectory?\n> regards,\n\nSince the atom is (microscopically) heavy it has (microscopically) large\nmomentum. Using the de Broglie relation between the momentum and the\ncharacteristic wavelength, lambda = h/p, we see that the atoms\ncharacteristic wavelength is very small.\n\nThink about wave and ray optics. Ray geometric optics approximates well\nthe propagation of short wavelength E&M radiation (say light). But the\nray approximation fails for large wavelengths (say radio waves).\nSimilar reasoning applies to the wave description of the atom. Here the\nray approximation corresponds to the approximation that classical\ntrajectories are well defined and correspond closely to the trajectory\nof the atom\'s wavepacket.\n\nHope this helps.\n\nIgor\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>On 2005-05-28, Ali <ph_question@yahoo.com> wrote:
> Dear Members,
>
> In Late Sakurai's " Modern Quantum Mechanics", in the description of
> Stern-Gerlach experiment, you read "Because the atom as a whole is very
> HEAVY, we expect that the CLASSICAL CONCEPT of trajectory can be
> legitimately applied, ... " (p.3) what is the relevance of "heaviness
> of atom" to classical concept of trajectory?
> regards,
Since the atom is (microscopically) heavy it has (microscopically) large
momentum. Using the de Broglie relation between the momentum and the
characteristic wavelength, \lambda = h/p, we see that the atoms
characteristic wavelength is very small.
Think about wave and ray optics. Ray geometric optics approximates well
the propagation of short wavelength E&M radiation (say light). But the
ray approximation fails for large wavelengths (say radio waves).
Similar reasoning applies to the wave description of the atom. Here the
ray approximation corresponds to the approximation that classical
trajectories are well defined and correspond closely to the trajectory
of the atom's wavepacket.
Hope this helps.
Igor
Hendrik van Hees
May29-05, 05:46 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>Igor Khavkine wrote:\n\n\n> Since the atom is (microscopically) heavy it has (microscopically)\n> large momentum. Using the de Broglie relation between the momentum and\n> the characteristic wavelength, lambda = h/p, we see that the atoms\n> characteristic wavelength is very small.\n\nOf course it depends on the circumstances whether you can treat a heavy\nparticle\'s motion classically or not. If you have well-isolated enough\nparticles (i.e. by suppression of any decoherence effects) and small\nenough "gratings" of what kind ever, also very heavy objects can behave\nquantum mechanically and show "wave character". This was demonstrated\nclearly by a now famous experiment by A. Zeilinger and collaborators:\nEven bucky balls (C_60 molecules) can show interference effects, which\nvanish if they become too hot and sending out black-body radiation.\n>\n> Think about wave and ray optics. Ray geometric optics approximates\n> well the propagation of short wavelength E&M radiation (say light).\n> But the ray approximation fails for large wavelengths (say radio\n> waves). Similar reasoning applies to the wave description of the atom.\n> Here the ray approximation corresponds to the approximation that\n> classical trajectories are well defined and correspond closely to the\n> trajectory of the atom\'s wavepacket.\n\nThat\'s of course right, as long as all the stuff around the atom has\nmeasures far larger than the de Broglie wave length, you can apply\nsingular perturbation theory and go to the classical limit (also known\nas WKBS method).\n\n--\nHendrik van Hees Texas A&M University\nPhone: +1 979/845-1411 Cyclotron Institute, MS-3366\nFax: +1 979/845-1899 College Station, TX 77843-3366\nhttp://theory.gsi.de/~vanhees/ mailto:hees@comp.tamu.edu\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>Igor Khavkine wrote:
> Since the atom is (microscopically) heavy it has (microscopically)
> large momentum. Using the de Broglie relation between the momentum and
> the characteristic wavelength, \lambda = h/p, we see that the atoms
> characteristic wavelength is very small.
Of course it depends on the circumstances whether you can treat a heavy
particle's motion classically or not. If you have well-isolated enough
particles (i.e. by suppression of any decoherence effects) and small
enough "gratings" of what kind ever, also very heavy objects can behave
quantum mechanically and show "wave character". This was demonstrated
clearly by a now famous experiment by A. Zeilinger and collaborators:
Even bucky balls (C_{60} molecules) can show interference effects, which
vanish if they become too hot and sending out black-body radiation.
>
> Think about wave and ray optics. Ray geometric optics approximates
> well the propagation of short wavelength E&M radiation (say light).
> But the ray approximation fails for large wavelengths (say radio
> waves). Similar reasoning applies to the wave description of the atom.
> Here the ray approximation corresponds to the approximation that
> classical trajectories are well defined and correspond closely to the
> trajectory of the atom's wavepacket.
That's of course right, as long as all the stuff around the atom has
measures far larger than the de Broglie wave length, you can apply
singular perturbation theory and go to the classical limit (also known
as WKBS method).
--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/ mailto:hees@comp.tamu.edu
Uncle Al
May30-05, 12:20 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>Ali wrote:\n>\n> Dear Members,\n>\n> In Late Sakurai\'s " Modern Quantum Mechanics", in the description of\n> Stern-Gerlach experiment, you read "Because the atom as a whole is very\n> HEAVY, we expect that the CLASSICAL CONCEPT of trajectory can be\n> legitimately applied, ... " (p.3) what is the relevance of "heaviness\n> of atom" to classical concept of trajectory?\n> regards,\n\nde Broglie wavelength. If your wavelengths approach the size of your\napertures you get spatial distribution structure from diffraction\n(e.g., Fourier transform of a round aperture to give an Airy circle\neven for TEM_00 monochromatic coherent light). This obviously did not\nobtain in the silver case in this apparatus. However, it can\nhappen...\n\nhttp://www.quantum.univie.ac.at/research/matterwave/c60/\n\n--\nUncle Al\nhttp://www.mazepath.com/uncleal/\n(Toxic URL! Unsafe for children and most mammals)\nhttp://www.mazepath.com/uncleal/qz.pdf\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>Ali wrote:
>
> Dear Members,
>
> In Late Sakurai's " Modern Quantum Mechanics", in the description of
> Stern-Gerlach experiment, you read "Because the atom as a whole is very
> HEAVY, we expect that the CLASSICAL CONCEPT of trajectory can be
> legitimately applied, ... " (p.3) what is the relevance of "heaviness
> of atom" to classical concept of trajectory?
> regards,
de Broglie wavelength. If your wavelengths approach the size of your
apertures you get spatial distribution structure from diffraction
(e.g., Fourier transform of a round aperture to give an Airy circle
even for TEM_00 monochromatic coherent light). This obviously did not
obtain in the silver case in this apparatus. However, it can
happen...
http://www.quantum.univie.ac.at/research/matterwave/c60/
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Arnold Neumaier
May31-05, 01:37 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>Ali wrote:\n\n> In Late Sakurai\'s " Modern Quantum Mechanics", in the description of\n> Stern-Gerlach experiment, you read "Because the atom as a whole is very\n> HEAVY, we expect that the CLASSICAL CONCEPT of trajectory can be\n> legitimately applied, ... " (p.3) what is the relevance of "heaviness\n> of atom" to classical concept of trajectory?\n> regards,\n\nThe heavier a particle, the more closely resembles it trajectory that of\na coherent state, which is essentially classical. You might find my\ndiscussion of the Stern-Gerlach experiment in my theoretical physics FAQ\nat\nhttp://www.mat.univie.ac.at/~neum/physics-faq.txt\nilluminating.\n\n\nArnold Neumaier\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>Ali wrote:
> In Late Sakurai's " Modern Quantum Mechanics", in the description of
> Stern-Gerlach experiment, you read "Because the atom as a whole is very
> HEAVY, we expect that the CLASSICAL CONCEPT of trajectory can be
> legitimately applied, ... " (p.3) what is the relevance of "heaviness
> of atom" to classical concept of trajectory?
> regards,
The heavier a particle, the more closely resembles it trajectory that of
a coherent state, which is essentially classical. You might find my
discussion of the Stern-Gerlach experiment in my theoretical physics FAQ
at
http://www.mat.univie.ac.at/~neum/physics-faq.txt
illuminating.
Arnold Neumaier
Igor Khavkine
Oct11-06, 03:04 PM
On 2005-05-28, Ali <ph_question@yahoo.com> wrote:
> Dear Members,
>
> In Late Sakurai's " Modern Quantum Mechanics", in the description of
> Stern-Gerlach experiment, you read "Because the atom as a whole is very
> HEAVY, we expect that the CLASSICAL CONCEPT of trajectory can be
> legitimately applied, ... " (p.3) what is the relevance of "heaviness
> of atom" to classical concept of trajectory?
> regards,
Since the atom is (microscopically) heavy it has (microscopically) large
momentum. Using the de Broglie relation between the momentum and the
characteristic wavelength, lambda = h/p, we see that the atoms
characteristic wavelength is very small.
Think about wave and ray optics. Ray geometric optics approximates well
the propagation of short wavelength E&M radiation (say light). But the
ray approximation fails for large wavelengths (say radio waves).
Similar reasoning applies to the wave description of the atom. Here the
ray approximation corresponds to the approximation that classical
trajectories are well defined and correspond closely to the trajectory
of the atom's wavepacket.
Hope this helps.
Igor
Hendrik van Hees
Oct11-06, 03:04 PM
Igor Khavkine wrote:
> Since the atom is (microscopically) heavy it has (microscopically)
> large momentum. Using the de Broglie relation between the momentum and
> the characteristic wavelength, lambda = h/p, we see that the atoms
> characteristic wavelength is very small.
Of course it depends on the circumstances whether you can treat a heavy
particle's motion classically or not. If you have well-isolated enough
particles (i.e. by suppression of any decoherence effects) and small
enough "gratings" of what kind ever, also very heavy objects can behave
quantum mechanically and show "wave character". This was demonstrated
clearly by a now famous experiment by A. Zeilinger and collaborators:
Even bucky balls (C_60 molecules) can show interference effects, which
vanish if they become too hot and sending out black-body radiation.
>
> Think about wave and ray optics. Ray geometric optics approximates
> well the propagation of short wavelength E&M radiation (say light).
> But the ray approximation fails for large wavelengths (say radio
> waves). Similar reasoning applies to the wave description of the atom.
> Here the ray approximation corresponds to the approximation that
> classical trajectories are well defined and correspond closely to the
> trajectory of the atom's wavepacket.
That's of course right, as long as all the stuff around the atom has
measures far larger than the de Broglie wave length, you can apply
singular perturbation theory and go to the classical limit (also known
as WKBS method).
--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/ mailto:hees@comp.tamu.edu
Uncle Al
Oct11-06, 03:04 PM
Ali wrote:
>
> Dear Members,
>
> In Late Sakurai's " Modern Quantum Mechanics", in the description of
> Stern-Gerlach experiment, you read "Because the atom as a whole is very
> HEAVY, we expect that the CLASSICAL CONCEPT of trajectory can be
> legitimately applied, ... " (p.3) what is the relevance of "heaviness
> of atom" to classical concept of trajectory?
> regards,
de Broglie wavelength. If your wavelengths approach the size of your
apertures you get spatial distribution structure from diffraction
(e.g., Fourier transform of a round aperture to give an Airy circle
even for TEM_00 monochromatic coherent light). This obviously did not
obtain in the silver case in this apparatus. However, it can
happen...
http://www.quantum.univie.ac.at/research/matterwave/c60/
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Arnold Neumaier
Oct11-06, 03:05 PM
Ali wrote:
> In Late Sakurai's " Modern Quantum Mechanics", in the description of
> Stern-Gerlach experiment, you read "Because the atom as a whole is very
> HEAVY, we expect that the CLASSICAL CONCEPT of trajectory can be
> legitimately applied, ... " (p.3) what is the relevance of "heaviness
> of atom" to classical concept of trajectory?
> regards,
The heavier a particle, the more closely resembles it trajectory that of
a coherent state, which is essentially classical. You might find my
discussion of the Stern-Gerlach experiment in my theoretical physics FAQ
at
http://www.mat.univie.ac.at/~neum/physics-faq.txt
illuminating.
Arnold Neumaier
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