%0 Journal Article %A Hallnas, Martin %A Langmann, Edwin %A Paufler, Cornelius %D 2013 %T Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles %U https://repository.lboro.ac.uk/articles/journal_contribution/Generalized_local_interactions_in_1D_solutions_of_quantum_many-body_systems_describing_distinguishable_particles/9385670 %2 https://repository.lboro.ac.uk/ndownloader/files/16998866 %K untagged %K Mathematical Sciences not elsewhere classified %X As is well known, there exists a four-parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum-dependent terms, and determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta-interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta and (the so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang–Baxter relations. For the other model we write down explicit formulae for all eigenfunctions. %I Loughborough University