Talk:Quantum harmonic oscillator

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What is the "happy property of the r^2 potential", referred to in the section on the N-dimensional oscillator? It seems to me that we can also separate the potential energy of (uncoupled) anharmonic oscillators into terms depending on one coordinate each. -- Jitse Niesen 19:03, 14 Mar 2004 (UTC)

In classical mechanics there are exactly two central potentials whose orbits in N dimensions are ellipses, r^2 and 1/r. The r^2 potential is also the only potential (in one dimension) leading to oscillations whose period is intependent of the amplitude of the oscillations. The Born-Sommerfeld semiclassical quantization relates these two nice properties of the classical potential r^2 to the fact that the energy levels of the quantum harmonic orcillator are equally spaced. Hope that helps. Miguel 19:09, 2004 Mar 14 (UTC)

Wow, that's a quick answer. I get the point, thanks. -- Jitse Niesen 19:37, 14 Mar 2004 (UTC)

Contents

[edit] 2 questions

I've deleted and transed it to copy at Wiki's reference desk.--HydrogenSu 12:10, 5 February 2006 (UTC)

"It is one of the most important model systems in quantum mechanics because, as in classical mechanics, a wide variety of physical situations can be reduced to it either exactly or approximately." Can be reduced to what? The word "it" is not specified as anything. It would be greatly appreciated if someone could clarify this sentence.

[edit] Fanifol revert

On 13 June 2006, a user named User:Fanifol apparently reverted the article to the state of 10 March 2006. This was Fanifol's only contribution to the wikipedia, and his revision comment was "THE CERTAINTY PRINCIPLE WAR [1]". However, as in the last nine days no other wikipedia editor has bothered to revert this edit, I now hesitate to do so. Could somebody please provide some background on "THE CERTAINTY PRINCIPLE WAR"? — Tobias Bergemann 14:22, 22 June 2006 (UTC)

After reading the discussion on Uncertainty principle I now assume User:Fanifol to be a sock puppet of the banned user Hryun. I am going to revert his revert. — Tobias Bergemann 14:28, 22 June 2006 (UTC)

[edit] error in diagram?

I think one of the diagrams (the one captioned as "Wavefunction representations for the first six bound eigenstates...") is incorrect. I was plotting Ψ for n=0..5 in maple for some work i'm doing and i noticed that my plots for n=2 and n=3 are reflected in the x axis relative to those shown in the article. This website [2]also agrees with my plots.

Have I missed something here, or are these actually wrong? If they are can some one fix them? Poobarb 17:15, 19 October 2006 (UTC)

The only difference is a minus sign in the wave function. Such things are irrelevant in QM. David Da Vit 09:06, 21 March 2007 (UTC)

[edit] Anharmonic oscillator

The cubic potential is rather awkward...it will result in an unbounded system! I removed it for now. I think it's better to rewrite that section with a quartic potential instead, and probably in a different article. --HappyCamper 16:03, 14 April 2007 (UTC)

[edit] 3-dimensional harmonic oscillator

This is why I edited the example of the 3-dimensional harmonic oscillator:

  • A few small spelling mistakes.
  • More importantly: a 3-dimensional harmonic oscillator is not necessarily isotropic. One can have different vibrational frequencies in different directions: \omega_x \ne \omega_y\ne \omega_z .
  • I changed inline TeX letters to html italic, because for some reason, unknown to me, the inline TeX came out roman.

--P.wormer 08:53, 25 May 2007 (UTC)