Equivalence of Local and Separable Realizations of the Discontinuity-Inducing Contact Interaction and Its Perturbative Renormalizability

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

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References in corpus (4)

• Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction
• Realizing Discontinuous Wave Functions with Renormalized Short-Range Potentials
• Double Spiral Energy Surface in One-dimensional Quantum Mechanics of Generalized Pointlike Potentials
• Spectral Properties of Three-Dimensional Quantum Billiards with a Pointlike Scatterer

Cited by in corpus (3)

• Green functions for generalized point interactions in 1D: A scattering approach
• Classical Aspects of Quantum Walls in One Dimension
• Continuous Spectra of Generalized Kronig-Penney Model