Level crossings of eigenvalues of the Schrodinger Hamiltonian of the isotropic harmonic¨ oscillator perturbed by a central point interaction in different dimensions
https://doi.org/10.17586/2220-8054-2018-9-2-179-186
Abstract
In this brief presentation, some striking differences between level crossings of eigenvalues in one dimension (harmonic or conic oscillator with a central nonlocal δ0-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.
Supporting agencies: S. Fassari wishes to acknowledge Prof. I. Popov’s kind invitation to present the main points of this article in one of the sessions of the conference “Mathematical Challenge of Quantum Transport in Nanosystems, Pierre Duclos Workshop”, held at ITMO University, Saint Petersburg, Russia (September 26-27, 2017). Stimulating discussions with Prof. M.J. Lopez and Prof. J. Negro are kindly acknowledged. Partial financial support is acknowledged to the Spanish Junta de Castilla y Leon and FEDER (Project VA057U16) and MINECO (Project´ MTM2014-57129-C2-1-P). S. Fassari and M.L. Glasser also wish to thank the entire staff at Departamento de F´ısica Teorica, At´ omica y´ Optica, Universidad de Valladolid, for their warm hospitality throughout their stays.´
About the Authors
S. Fassari
Departamento de F´ısica Teorica, At´omica y´ Optica; CERFIM; Dipartimento di Fisica Nucleare, Subnucleare e delle Radiazioni, Univ. degli Studi Guglielmo Marconi
Spain
Spain
U. Valladolid, 47011 Valladolid
PO Box 1132, Via F. Rusca 1, CH-6601 Locarno, Switzerland
Via Plinio 44, I-00193 Rome, Italy
M. Gadella
Departamento de F´ısica Teorica, At´omica y´ Optica
Spain
Spain
U. Valladolid, 47011 Valladolid
M. L. Glasser
Departamento de F´ısica Teorica, At´omica y´ Optica; Department of Physics, Clarkson University
Spain
Spain
U. Valladolid, 47011 Valladolid
Potsdam, NY, 13699 USA
L. M. Nieto
Departamento de F´ısica Teorica, At´omica y´ Optica
Spain
Spain
U. Valladolid, 47011 Valladolid
F. matfa62@gmail.com
CERFIM; Dipartimento di Fisica Nucleare, Subnucleare e delle Radiazioni, Univ. degli Studi Guglielmo Marconi
Switzerland
Switzerland
PO Box 1132, Via F. Rusca 1, CH-6601 Locarno
Via Plinio 44, I-00193 Rome, Italy
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Review
For citations:
Fassari S., Gadella M., Glasser M.L., Nieto L.M., matfa62@gmail.com F. Level crossings of eigenvalues of the Schrodinger Hamiltonian of the isotropic harmonic¨ oscillator perturbed by a central point interaction in different dimensions. Nanosystems: Physics, Chemistry, Mathematics. 2018;9(2):179–186. https://doi.org/10.17586/2220-8054-2018-9-2-179-186
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