On a non-separable quantum many-particle system on the half-line

In this paper we will report on a one-dimensional, non-separable quantum many-particle system. It consists of two (distinguishable) particles moving on the half-line $\mathbb{R}_+$ being subjected to two different kinds of two-particle interactions: singular many-particle interactions localized at the origin and a binding-potential leading to a molecular-like state. We will formulate the model precisely, obtaining a well-defined self-adjoint operator (the Hamiltonian for our system) and elaborate on its spectral properties. In addition, we will present possible directions for future research.