Spectral analysis of a two body problem with zero-range perturbation |
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| Authors: | M. Correggi G. Dell'Antonio |
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| Affiliation: | a Scuola Normale Superiore (SNS), P.zza dei Cavalieri 7, 56126 Pisa, Italy
b Dipartimento di Matematica, Università Di Roma “La Sapienza”, P.zza A. Moro 5, 00185 Rome, Italy |
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| 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. |
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| Keywords: | Solvable models in quantum mechanics Zero-range interactions |
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