Spectral Analysis of a Two Body Problem with Zero Range Perturbation

Details Spectral Analysis of a Two Body Problem with Zero Range Perturbation Spectral Analysis of a Two Body Problem with Zero Range Perturbation

2007-08-02

arxiv.org/abs/0708.0371v2

J. Funct. Anal. 255 (2008), 502-531

Physics

Mathematical Physics

Version submitted for publication, AMStex, 22 pages

Scientific paper

10.1016/j.jfa.2008.04.005

We consider a class of singular, zero-range perturbations of the Hamiltonian of a quantum system composed by a test particle and a harmonic oscillators in dimension one, two and three and we study its spectrum. In facts 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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