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Schrodinger Equation

  1. Aug 22, 2011 #1
    1. The problem statement, all variables and given/known data

    See attached photo


    3. The attempt at a solution

    So I have no idea if I have even started this problem correctly so any help would be nice.

    My working is set out in one of the pictures.

    Any help would be appreciated I really am not quite sure what to do. Can't figure out where the x^2-y^2 comes from.

    Thank you!
     

    Attached Files:

  2. jcsd
  3. Aug 23, 2011 #2

    tiny-tim

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    Hi KingBigness! :wink:
    I'm guessing really, since this isn't my field :redface:, but if you replace r2sin2θcos2φ by r2sin2θ(cos2φ - sin2φ), that looks like x2 - y2 :smile:
     
  4. Aug 23, 2011 #3

    vela

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    Leave the r2 alone for now and use the fact that[tex]\cos \theta = \frac{e^{i\theta} + e^{-i\theta}}{2}[/tex]to get rid of the complex exponentials.
     
  5. Aug 23, 2011 #4
    Thank you both for that, I shall try that and let you know how I go
     
  6. Aug 25, 2011 #5
    Ok I tried that and out came the x^2-y^2

    Thank you for that tip.

    This is the answer I have ended up with can you let me know if it is correct or if I need to simplify it more? not really sure when to stop =\
     

    Attached Files:

  7. Aug 25, 2011 #6
    I lied above....I brought the sin theta squared in before I converted which got rid of the sin theta squared in the final answer.

    Is this now correct?
     
  8. Aug 25, 2011 #7

    vela

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    Yes, that's right, because in spherical coordinates x = r sin θ cos φ and y = r sin θ sin φ.
     
  9. Aug 25, 2011 #8
    Sweet finally got this question complete!

    Thank you. Will double check all my algebra later to make sure I haven't done a silly mistake.

    Thanks again for your help
     
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