Two particles on a star graph I

TL;DR

This paper studies a two-particle quantum system on a star graph with delta interaction, deriving eigensolutions based on single-particle solutions, including some with discontinuous derivatives.

Contribution

It introduces a class of eigensolutions for two particles on a star graph with delta interaction, parametrized by two momenta, expanding understanding of such quantum systems.

Findings

Derived eigensolutions from one-particle solutions

Identified solutions with discontinuous derivatives on the diagonal

Parametrized solutions by two momenta

Abstract

We consider a two particle system on a star graph with $\delta$-function interaction. A class of eigensolutions is described which are constructed from appropriate one particle solutions, and hence are parametrised by two momenta. These solutions include a family of solutions with discontinuous derivative on the diagonal.