najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2018-9-2-179-186najo-690Research ArticleMATHEMATICSМАТЕМАТИКАLevel crossings of eigenvalues of the Schrodinger Hamiltonian of the isotropic harmonic¨ oscillator perturbed by a central point interaction in different dimensionsFassariS.

U. Valladolid, 47011 Valladolid

PO Box 1132, Via F. Rusca 1, CH-6601 Locarno, Switzerland

Via Plinio 44, I-00193 Rome, Italy

silvestro.fassari@uva.esGadellaM.

U. Valladolid, 47011 Valladolid

gadella@fta.uva.esGlasserM. L.

U. Valladolid, 47011 Valladolid

Potsdam, NY, 13699 USA

laryg@tds.netNietoL. M.

U. Valladolid, 47011 Valladolid

 

luismiguel.nieto.calzada@uva.esMatfa62@gmail.comF.

PO Box 1132, Via F. Rusca 1, CH-6601 Locarno

Via Plinio 44, I-00193 Rome, Italy

Departamento de F´ısica Teorica, At´omica y´ Optica; CERFIM; Dipartimento di Fisica Nucleare, Subnucleare e delle Radiazioni, Univ. degli Studi Guglielmo MarconiSpainDepartamento de F´ısica Teorica, At´omica y´ OpticaSpainDepartamento de F´ısica Teorica, At´omica y´ Optica; Department of Physics, Clarkson UniversitySpainCERFIM; Dipartimento di Fisica Nucleare, Subnucleare e delle Radiazioni, Univ. degli Studi Guglielmo MarconiSwitzerland20181208202592179–186Copyright © Fassari S., Gadella M., Glasser M.L., Nieto L.M., matfa62@gmail.com F., 20252025Fassari S., Gadella M., Glasser M.L., Nieto L.M., matfa62@gmail.com F.Fassari S., Gadella M., Glasser M.L., Nieto L.M., matfa62@gmail.com F.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/690

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.

harmonic oscillatorpoint interactionsrenormalisationeigenvalueslevel crossingS. 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.´ReferencesAlbeverio S., Gesztesy F., Høegh-Krohn R., Holden H. 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The authors declare that there are no conflicts of interest present.