TL;DR
This paper provides a comprehensive analysis of a two-particle quantum system on a star graph with delta interactions, detailing eigensolutions with real momenta and expressing them through integrals of one-particle solutions.
Contribution
It offers a complete characterization of eigensolutions for two particles on a star graph with delta interactions, extending previous work with explicit integral representations.
Findings
All eigensolutions can be expressed as integrals over the momentum plane.
Eigensolutions are representable as sums of products of one-particle solutions.
The paper fully describes eigensolutions with real momenta.
Abstract
We consider a two particle system on a star graph with delta-function interaction. A complete description of the eigensolutions with real momenta is given; specifically it is shown that all eigensolutions can be written as integrals in the momentum plane of sums of products of appropriate one particle solutions.
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