 03233 Dell'Antonio G., Finco D., Teta A.
 Singularly Perturbed Hamiltonians of a Quantum Rayleigh Gas
Defined as Quadratic Forms
(87K, LATeX 2e)
May 22, 03

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Abstract. We consider a class of singular, zerorange
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 selfadjoint 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.
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