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Homework Help: 3-dimensional harmonic oscillator (quantum mechanics)

  1. Apr 28, 2009 #1
    1. The problem statement, all variables and given/known data

    3-dimensional harmonic oscillator has a potetnial energy of [tex]U(x,y,z)=\frac{1}{2}k'(x^2+y^2+z^2)[/tex].
    a) Determine the energy levels of the oscillator as a function of angular velocity.
    b) Calculate the value for the ground state energy and the separation between adjacent energy levels.

    2. Relevant equations

    [tex]-\frac{\hbar^2}{2m}\nabla ^2\psi+U\psi=E\psi[/tex]

    3. The attempt at a solution

    We have a wave function [tex]\psi=\psi(x,y,z)[/tex]. I plug it in the equation and get nothing that helps me, since I don't know the function. Any suggestions?
  2. jcsd
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