Question: For helium the first-order perturbation energy correction is e2/4((0r12 averaged over the correct unperturbed wave function. Show that if we evaluate (e2/4((0r12) using the incorrect

For helium the first-order perturbation energy correction is e2/4((0r12 averaged over the correct unperturbed wave function. Show that if we evaluate (e2/4((0r12) using the incorrect zeroth-order functions 1s(1)2s(2) or 1s(2)2s(1), we get J1s2s in each case. Now show that when we use the correct functions (9.103) and (9.104) to evaluate (e2/4((0r12), we get J1s2s ( K1s2s (as found from the secular equation). The exchange-integral contribution to the energy thus arises from the indistinguishability of electrons in the same atom.

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