NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2019, 10 (6), P. 608–615
Exact calculation of the trace of the Birman–Schwinger operator of the one-dimensional harmonic oscillator perturbed by an attractive Gaussian potential
S. Fassari – Department of Higher Mathematics, ITMO University, St. Petersburg, Russia; CERFIM, PO Box 1132, 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
F. Rinaldi – CERFIM, PO Box 1132, CH-6601 Locarno, Switzerland; Dipartimento di Fisica Nucleare, Subnucleare e delle Radiazioni, Univ. degli Studi Guglielmo Marconi,Via Plinio 44, I-00193 Rome, Italy; Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Naples, Italy; f.rinaldi@unimarconi.it
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.
DOI 10.17586/2220-8054-2019-10-6-608-615
