For a non-degenerate time indepedent perturbation, show that the first-order energy shift is equal to the expectation value of the perturbing Hamiltonian in the unperturbed energy eigenstate.

In atomic and molecular physics, perturbation theory is used to solve quantum systems that are subject to small disturbances. Consider a quantum system with a Hamiltonian H0H_0 describing the unperturbed system, and a perturbation H′H' that slightly ________ _______ _________ ________ __________.
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