The Hamiltonian of the harmonic oscillator with an attractive $\delta ^{\prime} $-interaction centred at the origin as approximated by the one with a triple of attractive $\delta $-interactions

DOI10.1088/1751-8113/49/2/025302zbMath1342.81100OpenAlexW2291676203MaRDI QIDQ2994550

Fabio Rinaldi, Silvestro Fassari, Sergio A. Albeverio

Publication date: 2 August 2016

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1751-8113/49/2/025302

zbMATH Keywords

Schrödinger operators point interactions perturbed quantum oscillators renomalisation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

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Conditions for realizing one-point interactions from a multi-layer structure model ⋮ Regularization of a strong–weak duality between pointlike interactions in one dimension ⋮ The spectrum of the Schrödinger–Hamiltonian for trapped particles in a cylinder with a topological defect perturbed by two attractive delta interactions ⋮ On the spectrum of two-particle Schrödinger operator with point interaction ⋮ Two-parametric ${\delta'}$ -interactions: approximation by Schrödinger operators with localized rank-two perturbations ⋮ The variational method applied to the harmonic oscillator in the presence of a delta function potential ⋮ On the spectrum of the one-particle Schrödinger operator with point interaction ⋮ Schrödinger operators with singular rank-two perturbations and point interactions ⋮ On the spectrum of the two-particle Schrödinger operator with point interaction ⋮ The quantum harmonic oscillator and Catalan's constant ⋮ Scattering data and bound states of a squeezed double-layer structure

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