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.

• Received 5 March 1984

DOI:https://doi.org/10.1103/PhysRevD.30.1233