Multiparticle Schrödinger Hamiltonians with point interactions

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Abstract
We construct the resolvent for a nonrelativistic multiparticle Schrödinger Hamiltonian having point interactions, and accommodating annihilation and creation of, at most, three particles. The construction is similar to that for the simple point-interaction (pseudopotential) case and leads to Skorniakov-Ter Martirosian-type integral equations. Unlike the Skorniakov-Ter Martirosian equations, however, the integral equations considered here have a unique solution and, moreover, the resulting Hamiltonian is bounded below. Scattering theory for the operator is discussed briefly.