Nth order perturbation theory for hydrogen

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Abstract
This paper presents a simple reformulation of second order perturbation theory for hydrogen. We calculate first the perturbed wavefunction and then the perturbed matrix element. This procedure is repeated to obtain the nth order matrix element in terms of n−1 integrals. The parameters in the nth order matrix element are defined recursively. Schwinger’s representation of the Coulomb Green’s function follows immediately from our expression for the second order matrix element.

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