- #1
Nastenka
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Homework Statement
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?
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...