NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2018, 9 (2), P. 179–186
Level crossings of eigenvalues of the Schrödinger Hamiltonian of the isotropic harmonic oscillator perturbed by a central point interaction in different dimensions
S. Fassari – Departamento de Física Teo´rica, Atómica y Óptica, U. Valladolid, 47011 Valladolid, Spain; CERFIM, PO Box 1132, Via F. Rusca 1, CH-6601 Locarno, Switzerland; Dipartimento di Fisica Nucleare, Subnucleare e delle Radiazioni, Univ. degli Studi Guglielmo Marconi, Via Plinio 44, I-00193 Rome, Italy; silvestro.fassari@uva.es
M. Gadella – Departamento de Física Teórica, Atómica y Óptica, U. Valladolid, 47011 Valladolid, Spain; gadella@fta.uva.es
M. L. Glasser – Departamento de Física Teórica, Atómica y Óptica, U. Valladolid, 47011 Valladolid, Spain; Department of Physics, Clarkson University, Potsdam, NY, 13699 USA; laryg@tds.net
L. M. Nieto – Departamento de Física Teórica, Atómica y Óptica, U. Valladolid, 47011 Valladolid, Spain ; luismiguel.nieto.calzada@uva.es
F. Rinaldi – CERFIM, PO Box 1132, Via F. Rusca 1, CH-6601 Locarno, Switzerland; Dipartimento di Fisica Nucleare, Subnucleare e delle Radiazioni, Univ. degli Studi Guglielmo Marconi, Via Plinio 44, I-00193 Rome, Italy; matfa62@gmail.com
In this brief presentation, some striking differences between level crossings of eigenvalues in one dimension (harmonic or conic oscillator with a central nonlocal δ’-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
DOI 10.17586/2220-8054-2018-9-2-179-186
