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Ground-state wave function

  1. Mar 4, 2007 #1
    1. The problem statement, all variables and given/known data

    Use the ground-state wave function of the simple harmonic oscillator to find: Xav, (X^2)av and deltaX. Use the normalization constant A= (m*omegao/(h_bar*pi))^1/4.

    2. Relevant equations

    deltaX=sqrt((X^2)av-(Xav)^2)

    wavefunc=A*e^(-ax^2) ?

    3. The attempt at a solution

    I'm not sure if I'm on the right path, but I started out by plugging in A and doing the integral of the wavefunction. My question is... does doing this give me Xav? If not, how would I go about solving this problem?
     
  2. jcsd
  3. Mar 4, 2007 #2

    Dick

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    If you plug the right A in and do the integral of [tex]\psi^* \psi[/tex] you should get 1. It's normalized. Getting <x>=Xav? requires inserting an x into the integral.

    [tex]<f(x)>=\int \psi^*(x) f(x) \psi(x) dx[/tex]
     
    Last edited: Mar 5, 2007
  4. Mar 5, 2007 #3

    Meir Achuz

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    Of course, you know you need to use Psi^2.
     
  5. Mar 5, 2007 #4

    Dick

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    I said that in a pretty sloppy way. I've edited the post to clarify.
     
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