Related papers: The two lowest eigenvalues of the harmonic oscillator in the presence of a Gaussian perturbation

The two lowest eigenvalues of the harmonic oscillator in the presence of a Gaussian perturbation

URL: http://arxiv.org/abs/2005.09245v1
Date: Tue, 19 May 2020 06:54:06 GMT
Title: The two lowest eigenvalues of the harmonic oscillator in the presence of a Gaussian perturbation
Authors: Silvestro Fassari, Luis M. Nieto and Fabio Rinaldi
Abstract summary: We consider a one-dimensional quantum mechanical particle constrained by a parabolic well perturbed by a Gaussian potential. As the related Birman-Schwinger operator is trace class, the Fredholm can be exploited in order to compute the modified eigenenergies.
Score: 4.168157981135698
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: In this note we consider a one-dimensional quantum mechanical particle constrained by a parabolic well perturbed by a Gaussian potential. As the related Birman-Schwinger operator is trace class, the Fredholm determinant can be exploited in order to compute the modified eigenenergies which differ from those of the harmonic oscillator due to the presence of the Gaussian perturbation. By taking advantage of Wang's results on scalar products of four eigenfunctions of the harmonic oscillator, it is possible to evaluate quite accurately the two lowest-lying eigenvalues as functions of the coupling constant $\lambda$.

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