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.
Correggi, M., Dell'Antonio, G., Finco, D. (2008). Spectral analysis of a two body problem with zero-range perturbation. JOURNAL OF FUNCTIONAL ANALYSIS, 255, 502-531 [10.1016/j.jfa.2008.04.005].
Spectral analysis of a two body problem with zero-range perturbation
CORREGGI, MICHELE;
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
