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Time-Dependent Perturbation Theory - Two-level System

  1. Mar 16, 2009 #1
    1. The problem statement, all variables and given/known data

    See attached. The problem is labeled "Peatross 1". Don't worry, it's short. I just didn't feel like retyping it.


    2. Relevant equations

    Included in attempt.


    3. The attempt at a solution

    I'm not sure if I am doing this correctly, but here it goes.

    I'll just do it for [tex]H'_{10}[/tex], since the method will be the same for both.

    I think all I have to do is calculate [tex]\psi_0[/tex] and [tex]\psi_1[/tex] using the following formula (for a harmonic oscillator):

    [tex]\left\langle x | \psi_n \right\rangle = \sqrt{\frac{1}{2^n\,n!}} \cdot \left(\frac{m\omega}{\pi \hbar}\right)^{1/4} \cdot \exp
    \left(- \frac{m\omega x^2}{2 \hbar} \right) \cdot H_n\left(\sqrt{\frac{m\omega}{\hbar}} x \right)[/tex]

    Then just compute the resulting integral (probably in Mathematica):

    [tex]\int_{- \infty}^{\infty} \psi_0 exE_0 \sin{\omega_L t\psi_1^*} dx[/tex]

    Is this all there is to it, or am I missing something?

    Thanks for your help!
     

    Attached Files:

    Last edited: Mar 16, 2009
  2. jcsd
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