We consider a class of singular, zero-range perturbations of the quantum Hamiltonian of a system consisting of a test particle and N harmonic oscillators (Rayleigh gas). Using the theory of quadratic forms we construct the self-adjoint and bounded from below perturbed Hamiltonian and we give representation formulas for the resolvent and the unitary group. The one-dimensional, two-dimensional and three-dimensional cases are discussed.
Singularly perturbed hamiltonians of a quantum Rayleigh gas defined as quadratic forms / Dell'Antonio, Gianfausto; Domenico, Finco; Teta, Alessandro. - In: POTENTIAL ANALYSIS. - ISSN 0926-2601. - STAMPA. - 22:3(2005), pp. 229-261. [10.1007/s11118-004-6121-y]
Singularly perturbed hamiltonians of a quantum Rayleigh gas defined as quadratic forms
DELL'ANTONIO, Gianfausto;TETA, Alessandro
2005
Abstract
We consider a class of singular, zero-range perturbations of the quantum Hamiltonian of a system consisting of a test particle and N harmonic oscillators (Rayleigh gas). Using the theory of quadratic forms we construct the self-adjoint and bounded from below perturbed Hamiltonian and we give representation formulas for the resolvent and the unitary group. The one-dimensional, two-dimensional and three-dimensional cases are discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
