This article is cited in 10 papers

MATHEMATICS

Level crossings of eigenvalues of the Schrödinger Hamiltonian of the isotropic harmonic oscillator perturbed by a central point interaction in different dimensions

S. Fassari^abc, M. Gadella^a, M. L. Glasser^ad, L. M. Nieto^a, F. Rinaldi<sup>bc

a</sup> Departamento de Física Teorica, Atómica y Óptica, U. Valladolid, 47011 Valladolid, Spain
^b CERFIM, PO Box 1132, Via F. Rusca 1, CH-6601 Locarno, Switzerland
^c Dipartimento di Fisica Nucleare, Subnucleare e delle Radiazioni, Univ. degli Studi Guglielmo Marconi, Via Plinio 44, I-00193 Rome, Italy
^d Department of Physics, Clarkson University, Potsdam, NY, 13699 USA

Abstract: In this brief presentation, some striking differences between level crossings of eigenvalues in one dimension (harmonic or conic oscillator with a central nonlocal $\delta'$-interaction) or three dimensions (isotropic harmonic oscillator with a three-dimensional delta located at the origin) and those occurring in the two-dimensional analogue of these models will be highlighted.

Keywords: harmonic oscillator, point interactions, renormalisation, eigenvalues, level crossing.

PACS: 02.30.Gp, 02.30.Lt, 02.30.Sa, 02.30.Tb, 03.65.Db, 03.65.Ge, 68.65.Hb

Received: 08.01.2018
Revised: 24.01.2018

Language: English

DOI: 10.17586/2220-8054-2018-9-2-179-186

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