Spectral properties of the two-dimensional Schrödinger Hamiltonian with various solvable confinements in the presence of a central point perturbation

We study three solvable two-dimensional systems perturbed by a point interaction centered at the origin. The unperturbed systems are the isotropic harmonic oscillator, a square pyramidal potential and a combination thereof. We study the spectrum of the perturbed systems. We show that, while most eig...

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Bibliographic Details
Published in:Physica scripta 2019-05, Vol.94 (5), p.55202
Main Authors: Fassari, S, Gadella, M, Glasser, M L, Nieto, L M, Rinaldi, F
Format: Article
Language:English
Subjects:
confining potentials
level crossing
point interaction
solvable models
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Summary:We study three solvable two-dimensional systems perturbed by a point interaction centered at the origin. The unperturbed systems are the isotropic harmonic oscillator, a square pyramidal potential and a combination thereof. We study the spectrum of the perturbed systems. We show that, while most eigenvalues are not affected by the point perturbation, a few of them are strongly perturbed. We show that for some values of one parameter, these perturbed eigenvalues may take lower values than the immediately lower eigenvalue, so that level crossings occur. These level crossings are studied in some detail.
ISSN:0031-8949
1402-4896
DOI:10.1088/1402-4896/ab0589