We consider a class of singular, zero-range perturbations of the Hamiltonian of a quantum system composed by a test particle and a harmonic oscillator in dimension one, two and three and we study its spectrum. In fact we give a detailed characterization of point spectrum and its asymptotic behavior with respect to the parameters entering the Hamiltonian. We also partially describe the positive spectrum and scattering properties of the Hamiltonian. © 2008 Elsevier Inc. All rights reserved.

Spectral analysis of a two body problem with zero-range perturbation

Correggi M.;
2008-01-01

Abstract

We consider a class of singular, zero-range perturbations of the Hamiltonian of a quantum system composed by a test particle and a harmonic oscillator in dimension one, two and three and we study its spectrum. In fact we give a detailed characterization of point spectrum and its asymptotic behavior with respect to the parameters entering the Hamiltonian. We also partially describe the positive spectrum and scattering properties of the Hamiltonian. © 2008 Elsevier Inc. All rights reserved.
Solvable models in quantum mechanics; Zero-range interactions
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1134391
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