How to calculate the transition rate

  1. 1. The problem statement, all variables and given/known data
    I have the usual equation for the transition amplitude:
    A=< k|exp(-iHt)| j>,


    while my Hamiltonian in Dirac notation looks like:

    H=\sum E_a|a><a|+\sum_b (E_b|b><b|+V_1|0><b|+ V_2|b><0|)

    In order to find the transition rate I should take a derivative as:
    dA/dt, so that I will get something like:

    A=< k|-iH*exp(-iHt)| j>



    2. Relevant questions

    Now, my question is:

    how to treat it further?



    3. The attempt at a solution

    I know I should expand it with series for the exponent, but then I obtain in the middle this:
    -iH(1+H)=-iH-iH2 that confuses me. I feel I am stucked in such an easy task. But the proble is that I cannot expand it with eigenvalues and eigenvectors which would simplify a lot my task....
     
  2. jcsd
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