New perturbation method with the matching of wave functions

Details New perturbation method with the matching of wave functions New perturbation method with the matching of wave functions

1998-12-14

arxiv.org/abs/quant-ph/9812027v2

Int. J. Quant. Phys. 79 (2000) 235 - 242

Physics

Quantum Physics

19 pages, 1 figure, text re-submitted to Int. J. Quant. Chem

Scientific paper

We propose a new approach to the Rayleigh-Schr\"{o}dinger perturbation expansions of bound states in quantum mechanics. We are inspired by the enormous flexibility of solvable interactions with several (N) discontinuities. Their standard matching solution is modified and transferred in perturbation regime. We employ the global renormalization freedom of the local wave functions and derive a compact N-dimensional matrix formula for corrections. In applications, our recipe is shown non-numerical for all polynomial perturbations of any piece-wise constant zero order potential.

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