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Nanosystems: Physics, Chemistry, Mathematics, 2019, Volume 10, Issue 6, Pages 608–615
DOI: https://doi.org/10.17586/2220-8054-2019-10-6-608-615 (Mi nano474) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Exact calculation of the trace of the Birman–Schwinger operator of the one-dimensional harmonic oscillator perturbed by an attractive Gaussian potential

S. Fassariabc, F. Rinaldidba

a CERFIM, PO Box 1132, CH-6601 Locarno, Switzerland
b Dipartimento di Fisica Nucleare, Subnucleare e delle Radiazioni, Univ. degli Studi Guglielmo Marconi, Via Plinio 44, I-00193 Rome, Italy
c Department of Higher Mathematics, ITMO University, St. Petersburg, Russia
d Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Naples, Italy
Full-text PDF (5111 kB) Citations (2)
DOI: https://doi.org/10.17586/2220-8054-2019-10-6-608-615
Abstract: By taking advantage of Wang’s results on the scalar product of four eigenfunctions of the 1D harmonic oscillator, we explicitly calculate the trace of the Birman–Schwinger operator of the one-dimensional harmonic oscillator perturbed by a Gaussian potential, showing that it can be written as a ratio of Gamma functions.
Keywords: Gaussian potential, Birman-Schwinger operator, trace class operator, harmonic oscillator.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
The final part of S. Fassari’s contribution to this work has been financially supported by the Government of the Russian Federation through the ITMO University Fellowship and Professorship Programme.
Received: 04.11.2019
Bibliographic databases:
Document Type: Article
Language: English
Citation: S. Fassari, F. Rinaldi, “Exact calculation of the trace of the Birman–Schwinger operator of the one-dimensional harmonic oscillator perturbed by an attractive Gaussian potential”, Nanosystems: Physics, Chemistry, Mathematics, 10:6 (2019), 608–615
Citation in format AMSBIB
\Bibitem{FasRin19}
\by S.~Fassari, F.~Rinaldi
\paper Exact calculation of the trace of the Birman--Schwinger operator of the one-dimensional harmonic oscillator perturbed by an attractive Gaussian potential
\jour Nanosystems: Physics, Chemistry, Mathematics
\yr 2019
\vol 10
\issue 6
\pages 608--615
\mathnet{http://mi.mathnet.ru/nano474}
\crossref{https://doi.org/10.17586/2220-8054-2019-10-6-608-615}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000504855900001}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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