## QM oscillator - a question for experimental verification

<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>It is well known that QM gives a wave structure of the probability\ndensity for the presence of a quantum oscillator in a box. Has anyone\nchecked this?\nI mean has anyone made a straightforward experiment to check if there\nare nodes of zero presence, by example sending a laser beam through\nthe nodes?\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>It is well known that QM gives a wave structure of the probability
density for the presence of a quantum oscillator in a box. Has anyone
checked this?
I mean has anyone made a straightforward experiment to check if there
are nodes of zero presence, by example sending a laser beam through
the nodes?



Kevin Blake wrote: > > It is well known that QM gives a wave structure of the probability > density for the presence of a quantum oscillator in a box. Has anyone > checked this? > I mean has anyone made a straightforward experiment to check if there > are nodes of zero presence, by example sending a laser beam through > the nodes? 1) What is an observable? It is $\psi^2$. You won't see "waves." You should see nodes and antinodes. 2) A literal "particle in a box" does exactly that. Standing waves, laser modes, microwave conduit... literal electrons confined in semiconductors. 3) Look up the experiment of dropping ultracryogenic neutrons and watching them bounce. Their bounce heights were quantized. Neutrons are fermions, spin 1/2. In a gravitational potetial well their allowed energy levels must stack. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf



On $2005-06-24,$ Kevin Blake wrote: > It is well known that QM gives a wave structure of the probability > density for the presence of a quantum oscillator in a box. Has anyone > checked this? > I mean has anyone made a straightforward experiment to check if there > are nodes of zero presence, by example sending a laser beam through > the nodes? When it comes to measuring very small or very cold things, where quantum mechanics is most prominent, little is straightforward. Are you referring specifically to a system that is well approximated by a simple harmonic oscillator? Or do you mean just any particle in a box or a confining potential? For the latter, Uncle Al already gave a couple of examples. For the former, it's a bit harder to come up with examples. The best place to find them would be in atomic physics. People working with trapped ions often work with harmonic traps. Sometimes they even place single ions into a harmonic well and cool it into (or close to) the ground state. Unfortunately, atoms are small so it's hard to actually measure the probability density in such a configuration. Although, somone has probably tried to measure it, I just can't point there. The same is done in Bose-Einstein condensates (BECs). In this case many atoms get put into a harmonic well and are cooled until all of them (pretty much) are in the ground state. Since they are bosons, in this case a single wave function is sufficient to describe their state. The Gaussian shape you see in articles about BECs can be thought of as this wave function (in momentum space) in the simple harmonic oscillator ground state. Unfortunately, it's hard to place a BEC into, say, the first excited state of the harmonic trap. Sorry, no nodes. Hope this helps. Igor

## QM oscillator - a question for experimental verification

<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>Kevin Blake &lt;kvblake2003@yahoo.com&gt; wrote:\n&gt; It is well known that QM gives a wave structure of the probability\n&gt; density for the presence of a quantum oscillator in a box. Has anyone\n&gt; checked this?\n&gt; I mean has anyone made a straightforward experiment to check if there\n&gt; are nodes of zero presence, by example sending a laser beam through\n&gt; the nodes?\n\nPerhaps the closest to what you\'re looking for is called\n"quantum state tomography", pioneered by the group of\nMike Raymer in Oregon, if I recall correctly.\n\nTry this as an original reference:\n\nhttp://prola.aps.org/abstract/PRL/v70/i9/p1244_1\n\nMeasurement of the Wigner distribution and the density matrix\nof a light mode using optical homodyne tomography: Application\nto squeezed states and the vacuum\n\nD. T. Smithey, M. Beck, M. G. Raymer, A. Faridani\n\nProbably there are some more popular treatments, and more up to\ndate ones floating about on the web somewhere. Try your favourite\nsearch engine...\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\nPublic Key: http://www.qols.ph.ic.ac.uk/~kinsle/key/work-key-2002a\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>Kevin Blake <kvblake2003@yahoo.com> wrote:
> It is well known that QM gives a wave structure of the probability
> density for the presence of a quantum oscillator in a box. Has anyone
> checked this?
> I mean has anyone made a straightforward experiment to check if there
> are nodes of zero presence, by example sending a laser beam through
> the nodes?

Perhaps the closest to what you're looking for is called
"quantum state tomography", pioneered by the group of
Mike Raymer in Oregon, if I recall correctly.

Try this as an original reference:

http://prola.aps.org/abstract/PRL/v70/i9/p1244_1

Measurement of the Wigner distribution and the density matrix
of a light mode using optical homodyne tomography: Application
to squeezed states and the vacuum

D. T. Smithey, M. Beck, M. G. Raymer, A. Faridani

Probably there are some more popular treatments, and more up to
search engine...

--
---------------------------------+---------------------------------
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/

Public Key: http://www.qols.ph.ic.ac.uk/~kinsle/key/work-key-2002a