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arXiv:quant-ph/9811083 · Journal of the Physical Society of Japan

Equivalence of Local and Separable Realizations of Discontinuity-Inducing Contact Interaction

Taksu Cheon, Takaomi Shigehara, Kazuo Takayanagi

Published Feb 15, 2000• 10 citations
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Abstract

We prove that the separable and local approximations of the discontinuity-inducing zero-range interaction in one-dimensional quantum mechanics are equivalent. We further show that the interaction allows the perturbative treatment through the coupling renormalization. Keywords: one-dimensional system, generalized contact interaction, renormalization, perturbative expansion. PACS Nos: 3.65.-w, 11.10.Gh, 31.15.Md

DOI
10.1143/jpsj.69.345

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We propose a new approach to the Rayleigh–Schrödinger 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 piecewise constant zero-order potential. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 235–242, 2000
We propose a new approach to the Rayleigh–Schrödinger 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 piecewise constant zero-order potential. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 235–242, 2000