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)