The application of Pade approximants in Rayleigh-Schrodinger perturbation theory is interpreted as making use of the freedom of choice for the orthogonality integrals between the unperturbed (zero-order) wavefunction and the higher-order wavefunctions. With this interpretation, approximants are found for the wavefunction as well as the energy and these provide more satisfactory wavefunctions than are given by the perturbation series itself.
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A. T. Amos (1978) studied this question.
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