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Quantum Mechanics 3D harmonic oscillator

  1. Jan 30, 2012 #1
    What is the normalized ground-state energy eigenfunction for the three-dimensional harmonic oscillator

    V(r) = 1/2 m* ω^2 * r^2

    Use seperation of varaibles strategy. Express the wave function in spherical coordinates. What is the orbital angualar momentum of the ground state? Explain?

    I am having a lot of trouble even knowing where to start. Any help would be appreciated. Thank you
     
  2. jcsd
  3. Jan 30, 2012 #2

    king vitamin

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    Have you seen Schrodinger's Equation in spherical coordinates before (e.g., the Hydrogen atom)?
     
  4. Jan 30, 2012 #3
    Yes I have. A long equation with partial derivatives
     
  5. Jan 30, 2012 #4

    vela

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    The problem tells you what to do. If you don't know what separation of variables is, I'd say start there by reading up about it.
     
  6. Jan 31, 2012 #5
    I use seperation of variables with regards to the r component? x^2 + y^2 + z^2 and then use the schrondiger equation and solve it that way? by converting the x y and z component into sperhical coordinates?
     
  7. Jan 31, 2012 #6
    nono
    Convert everything into spherical polar coordinates first, that wat the r component is just the r component, working with [itex]x^2+y^2+z^2[/itex] isn't really useful here (the potential is already in given spherical polar coordinates anyway, why convert back to cartesian?)

    Once you have done that, schrodingers equation should look something like the laplacian in spherical polar coordinates.
    Then you use seperation of variables [itex]\Psi (r,\theta,\phi)= R(r)Y(\theta,\phi)[/itex] and go from there
     
  8. Jan 31, 2012 #7

    vela

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    It's clear from what you wrote you don't understand what the method of separation of variables is, so I'll repeat my suggestion to read up on it.

    Your quantum mechanics textbook should cover how to solve the Schrodinger equation for the hydrogen atom. This problem is very similar to that one.
     
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