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Oscillation of a Bose Einstein condensate in an harmonic trap
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[QUOTE="DrClaude, post: 4547357, member: 461323"] That is correct. I don't see why you make an analogy based on the fact that the energy varies quadraticly with ##a##. I would rather argue that the GP energy acts here like a potential energy, and therefore use ##F = -\nabla U##. You then indeed get ##F = -N m \omega^2 a##. I think that it is at this point that you should make an analogy with the harmonic oscillator, since you get a force that is linear with respect to displacement. I'm not sure you can say anything about the modification of the "wave function" at this level of approximation. I'll have to think some more about it. (I put "wave function" in scare quotes because, although many use that vocabulary, it is actually incorrect. The ##\psi## following the Gross-Pitaevskii equation is not the wave function of the condensate, but rather the order parameter.) [/QUOTE]
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Oscillation of a Bose Einstein condensate in an harmonic trap
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