Dell'Antonio G., Finco D., Teta A.
Singularly Perturbed Hamiltonians of a Quantum Rayleigh Gas
Defined as Quadratic Forms
(87K, LATeX 2e)
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.