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I want to find the expectation value [tex]\langle x^2 \rangle[/tex] in

  1. Feb 13, 2005 #1
    I want to find the expectation value [tex]\langle x^2 \rangle[/tex] in some problem. To do this I make a change-of-variable,

    [tex]\xi = \sqrt{\frac{m\omega}{\hslash}}x,[/tex]​

    and compute the expectation value [tex]\langle \xi^2 \rangle[/tex] like this:

    [tex]\langle \xi^2 \rangle = \int\xi^2\vert\psi(\xi)\vert^2d\xi.[/tex]​

    Finally I change back to x:

    [tex]\langle \xi^2 \rangle = \langle \frac{m\omega}{\hslash}x^2 \rangle = \frac{m\omega}{\hslash}\langle x^2 \rangle \Rightarrow \langle x^2 \rangle = \frac{\hslash}{m\omega}\langle \xi^2 \rangle.[/tex]​

    I really can't see what is wrong here, but something is! I've tried it 10 times and I keep getting the wrong result.
     
  2. jcsd
  3. Feb 13, 2005 #2

    vanesch

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    Be carefull that your psi is still correctly normalized when expressed in xi !

    cheers,
    Patrick.
     
  4. Feb 13, 2005 #3
    Yep, that's it :D

    Thank you very much! How do you spot these things right away?
     
  5. Feb 13, 2005 #4

    vanesch

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    Because I'm an expert :blushing:

    An expert is someone who has made all possible and imaginable errors in a very small domain :rofl:

    cheers,
    Patrick.
     
  6. Feb 13, 2005 #5
    I see I'm on the right track, then... :rofl:
     
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