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Ground-state wave function

  • Thread starter GreenLRan
  • Start date
  • #1
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Homework Statement



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.

Homework Equations



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

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

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?
 

Answers and Replies

  • #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:
  • #3
Meir Achuz
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Of course, you know you need to use Psi^2.
 
  • #4
Dick
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Of course, you know you need to use Psi^2.
I said that in a pretty sloppy way. I've edited the post to clarify.
 

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