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I know how to prove the orthonormality of the hamiltonian when it is real but am struggling to work out how to prove it when the hamiltonian is not real.

When proving for a real hamiltonian the lefthand side equals zero as H(mn)=H(nm)complexconjugate. but if the hamiltonian is not real, i dont know how to proceed.

Can anybody help?

Thanks

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# Proof of orthonormality of the hamiltonian when not real

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