# Talk:Quantum harmonic oscillator

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The momentum operator p, I think, should be (h_bar / i)*(d/dx), not (-h_bar * i)*(d/dx). Source: Modern Physics, Tipler, 5th Ed. page 244. Cheers, Justin. —Preceding unsigned comment added by 67.160.211.137 (talk) 10:05, 15 December 2008 (UTC)

They're the same thing. 1/i = -i. Reedbeta (talk) 20:42, 26 February 2011 (UTC)

->I think the article would improve by adding a definition of w (omega) — Preceding unsigned comment added by Brenogalvaowp (talkcontribs) 10:19, 2 February 2012 (UTC)

Can someone please include a section on the damped, driven quantum harmonic oscillator? This would add tremendously to the content. Thank you. —Preceding unsigned comment added by 128.36.183.217 (talk) 21:24, 8 December 2008 (UTC)

Answer to the previous comment: The damped quantum harmonic oscillator is a far (!) more advanced subject than the undamped oscillator. In fact, it has been a research subject for the past 30 years... The difference in the level of sophistication needed (undamped vs. damped quantum osc.) is far greater than e.g. in the classical case (where one can simply add a friction force). So it is probably better to leave that out in this article. — Preceding unsigned comment added by 131.188.166.21 (talk) 17:06, 14 November 2012 (UTC)

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)

## 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.

## 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)

## 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 09:06, 21 March 2007 (UTC)

Well, the sign is not quite irrelevant, and it should be fixed: The minus sign becomes important when you use the annihilation/creation operator formalism to go down/up the ladder of states. Then every textbook has the convention that no minus sign appears in the matrix elements, i.e. a^dagger |n>=sqrt(n+1) |n+1>. This then fixes the relative signs of subsequent states (and only the overall sign of the ground state would be free to be chosen). And in this regard, the figure is unfortunately at least misleading, because readers will expect that the wave functions shown here are those that are stated further down in the article in terms of Hermite polynomials (which would have different signs).

## 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)

## 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)

I think that the normalization constant should be (re)written like this:

$N_{kl}=\sqrt{\sqrt{\left(\frac{2\nu}{\pi }\right)^{3}}\frac{2^{k+2l+3}\;k!\;\nu ^{l}}{ (2k+2l+1)!!}}\,$

For $\nu=1$:

Original formula integrated from r=0 to infty

New formula integrated from r=0 to infty — Preceding unsigned comment added by 192.135.11.195 (talk) 10:18, 30 May 2012 (UTC)

## "the zero of energy is not a physically meaningful quantity"

The article states "the lowest achievable energy is not zero...It is not obvious that this is significant, because normally the zero of energy is not a physically meaningful quantity, only differences in energies." If I'm not mistaken, the physically meaningful fact here is that the lowest energy is not equal to the minimum of the potential well. This is why there is zero-point "motion" in a QHO as opposed to a classical oscillator. We have set up the problem with the zero of energy at the bottom of the well, so when the ground state energy comes out as $\hbar \omega / 2$ all it means is that the ground state energy is higher than the bottom of the well - there is really no issue with the zero of energy not being physically meaningful. Unless anyone objects, I'll edit the article to make this clear. Reedbeta (talk) 20:33, 26 February 2011 (UTC)

I've made the change. Reedbeta (talk) 19:35, 27 February 2011 (UTC)