How to calculate the transition rateby Nastenka Tags: kets, quantum field theory, quantum mechanics 

#1
Jul1512, 09:47 AM

P: 1

1. The problem statement, all variables and given/known data
I have the usual equation for the transition amplitude: A=< kexp(iHt) j>, while my Hamiltonian in Dirac notation looks like: H=\sum E_aa><a+\sum_b (E_bb><b+V_10><b+ V_2b><0) In order to find the transition rate I should take a derivative as: dA/dt, so that I will get something like: A=< kiH*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)=iHiH^{2} 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.... 


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