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Kinetic and potential energy of harmonic oscillator

  1. Oct 7, 2007 #1
    1. The problem statement, all variables and given/known data
    Use ladder operator methods to determine the kinetic and potential energy of eigenstates of the harmonic oscillator.


    2. Relevant equations
    [tex]H=\frac{p^2}{2m} + \frac{1}{2}m\omega x^2[/tex]
    [tex]x=\sqrt{\frac{\hbar}{2m \omega}}(a+a^{\dagger})[/tex]


    3. The attempt at a solution
    So I squared x, and then substituted it in the expression for V:

    [tex]\langle n | V | n \rangle[/tex]

    I ended up getting [itex]V=\frac{1}{2}(n+\frac{1}{2})\hbar \omega[/itex]. This is one half of the energy expectation, so KE must be the same.

    I just dont have any references with me to confirm if this is right. Can anyone tell me? Thanks in advance. I could write out what I got V as, if someone wants, but if the answer is right, there may not be much point.
     
  2. jcsd
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