Abstract:
We consider a system of three quantum particles interacting by pairwise
short-range attraction potentials on a three-dimensional lattice (one of
the particles has an infinite mass). We prove that the number of bound
states of the corresponding Schrödinger operator is finite in the case
where the potentials satisfy certain conditions, the two two-particle
sub-Hamiltonians with infinite mass have a resonance at zero, and zero is
a regular point for the two-particle sub-Hamiltonian with finite mass.