Regularized Quadratic Forms for a Three Boson System with Zero-Range Interactions

Abstract

We present two possible strategies to obtain a lower bounded Hamiltonian for three bosons interacting through zero-range interactions. First, we investigate a family of zero-range Hamiltonians defined in a Hilbert space of tensorial wave functions. Then, we examine the regularizing effect of an ultraviolet cutoff on the boundary conditions satisfied by functions in the form domain of zero-range Hamiltonians of a three boson system.

Keywords

• Point interactions
• Three-body Hamiltonian
• Schr¨odinger operators