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A two-particle quantum system with zero-range interaction. (English) Zbl 1208.35121

Summary: We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally, we fully characterize the spectral properties of such operators.

MSC:

35Q40 PDEs in connection with quantum mechanics
35J10 Schrödinger operator, Schrödinger equation
35A30 Geometric theory, characteristics, transformations in context of PDEs
35P05 General topics in linear spectral theory for PDEs
81V25 Other elementary particle theory in quantum theory
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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