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klpskp

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In order to do that, one usually choses an orthonormal Basis ##|\psi_{i,j}>## of each ##S_i## with the property, that ##<\psi_{i,j}|V|\psi_{i,k}>=0## whenever ##j \neq k##. Let ##|\tilde{\psi}_{i,j}>## the first order correction of ##|\psi_{i,j}>##. Then pertubation theory gives

$$<\psi_{i',j'}|\tilde{\psi}_{i,j}>=\frac{<\psi_{i',j'}|V|\psi_{i,j}>}{E_{i}-E_{i'}}$$

when ##i'\neq i##

However, for ##i=i'## one doesn't obtain any information on ##<\psi_{i',j'}|\tilde{\psi}_{i,j}>##. What are the components of ##|\tilde{\psi}_{i,j}>## in ##S_i##?

Thank you :)