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Quantum Griffiths Example

  1. Oct 13, 2011 #1
    Find the expectation value of the potential energy in the nth state of the harmonic oscillator.

    This is his example 2.5 in the book, he uses a[itex]\pm[/itex]=1/Sqrt[2hmw]([itex]\mp[/itex]ip+mwx) to get x=Sqrt[h/2mw](a[itex]_{+}[/itex]+a[itex]_{-}[/itex])

    My question how does he do this? I can't seem to make the algebraic manipulations to get it into that form to follow out his example.
  2. jcsd
  3. Oct 13, 2011 #2


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    You have two equations, one for [itex]a_+[/itex] and one for [itex]a_-[/itex].

    All you have to do is solve them simultaneously for x and p. i.e. Solve one for x, solve the other for p, plug the first into the second, etc. etc.

    It may help to simplify things by defining some constants A and B such that:

    [tex]a_{\pm}=Ap\mp Bx[/tex]
  4. Oct 13, 2011 #3
    That was easy enough, thank you for the tip!
  5. Oct 13, 2011 #4


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    No problem! :smile:
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