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Parity violation potential

Physics Asked by BillKet on August 21, 2020

I read in several papers (e.g. this one) that if we have 2 levels of fixed, opposite parities, which are the eigenstates of a $P$,$T$-even Hamiltonian, and we add a perturbing potential which is $P$-odd, $T$-even, the matrix element of the new potential between the 2 states of opposite parity must be purely imaginary. How can I prove this?

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