03-233 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, 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.

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