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why i\hbar(\partial/\partialt+i\Omega)=i\hbarexp(-i\Omegat)\partial/\partialtexp(i\Omegat)

Homework Statement Homework Equations Suppose we have a single qubit principal system ,interacting with a single qubit environment through the transformation U=P0\otimesI+P1\otimesX where X is the usual Pauli matrix (acting on the enviornment)and P0=|0><0| ,P1=|1><1| are projectors...

I have been hanging on this problem for a long time without a solution! Suppose we have a single qubit principal system ,interacting with a single qubit environment through the transformation U=P0\otimesI+P1\otimesX where X is the usual Pauli matrix (acting on the enviornment)and P0=|0><0|...

For each symmetry operation R acting on a physical system,there is a corresponding unitary transformation U(R). But what is the principle for such relation? an example is that : for a continuous symmetry ,we can choose R infinitesimally close to the identity ,R=I+eT ,and the U is close to I...

thank you very much! thank you very much!

why? exp(ixA)=cos(x)I+isin(x)A if A*A=I