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 Reyleigh Gas Defined as Quadratic Forms
FINCO D;
2005-01-01
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.File in questo prodotto:
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