Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    G01

    User Avatar
    Homework Helper
    Gold Member

    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

    G01

    User Avatar
    Homework Helper
    Gold Member

    No problem! :smile:
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook