# Evaluating Transition probability between different states of Hydrogen atom

I am trying to evaluate the inner product $<2S_{\frac{1}{2}},F',F'_{3}|\delta^{3}(x)\sigma_{i}P_{i}|2P_{\frac{1}{2}},F,F_{3}>$ It's written in the form $<nl_{j},F,F_{3}|$ Where $P_{i}$ in the momemtum operator for electron wave function , $j$ is the total angular momemtum of electron and $F$,$F_{3}$ are the total angular momemtum and it's projection along z axis.I tried solving it using Clebsch Gordon coefficients but couldn't get the answer. Any idea on how to solve it?

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 Maybe I can answer this in about a year and a half if I get into grad school : ( sorry – Timtam Feb 12 '12 at 4:50 It looks like my answer for your previous question is not complete. I could write explicit expression for the total wavefunction. For that, please, answer my last comment here: physics.stackexchange.com/questions/20345/… – Maksim Zholudev Feb 12 '12 at 11:27