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Homework Help: Two dimensional asymmetric harmonic oscillator

  1. Mar 12, 2012 #1
    Let's say I have a 2D harmonic oscillator:

    1. The problem statement, all variables and given/known data
    The potential is of course defined by: V = 1/2m(Omegax)x^2 + 1/2m(Omegay)y^2

    2. Relevant equations

    Generally when doing a harmonic oscillator we find that in two dimensions the energy is just:

    (Nx+Ny+1)hbarOmega is the energy.

    How does this change when the Omegax and Omegay are not equal?

    3. The attempt at a solution

    Do we simply get the energy as...

    E = (Nx+1/2)hbarOmegax + (Ny+1/2)hhbarOmegay ?

    That would seem logical, but would like the clarification.
  2. jcsd
  3. Mar 12, 2012 #2


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    Science Advisor
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    Gold Member

    Your intuition is correct. You can work it out by considering a separable solution of the form [itex]\psi(x,y)= X(x)Y(y)[/itex].
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