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-iH^{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....