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Harmonic oscillator derivation of wave functions

  1. Jul 15, 2012 #1
    here is a link to the pdf file with my question and answershttp://dl.dropbox.com/u/2399196/harmonic%20osc.pdf

    i'm not sure where to start, because i dont want to assume anything that i haven't been given.
    i'm stuck on part (iv) where i have to derive explicit expressions for 2 wave functions.

    thanks!
     
  2. jcsd
  3. Jul 15, 2012 #2

    gabbagabbahey

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    Well, from your 2 expressions for [itex]H[/itex] you have

    [tex]\left( \frac{1}{2}\hat{p}^2+\frac{1}{2}\hat{x}^2\right) \Psi_0(x)=\hbar\left(\hat{N}+\frac{1}{2} \right)\Psi_0(x) = \frac{\hbar}{2}\Psi_0(x)[/tex]

    So, if you express [itex]\hat{p}^2[/itex] and [itex]\hat{x}^2[/itex] in the [itex]x[/itex]-basis, you will have a differential equation you can solve for [itex]\Psi_0(x)[/itex]
     
  4. Jul 16, 2012 #3
    Last edited: Jul 16, 2012
  5. Jul 16, 2012 #4

    vela

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    This is a topic covered in many quantum mechanics and mathematical methods texts. I'd suggest you start there.
     
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