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Many body problems with “spin”-related contact interactions. (English) Zbl 0978.81085

Summary: We study quantum mechanical systems with “spin”-related contact interactions in one dimension. The boundary conditions describing the contact interactions are dependent on the spin states of the particles. In particular, we investigate the integrability of \(N\)-body systems with \(\delta\)-interactions and point spin couplings. Bethe ansatz solutions, bound states and scattering matrices are explicitly given. The cases of generalized separated boundary condition and some Hamiltonian operators corresponding to special spin related boundary conditions are also discussed.

MSC:

81V70 Many-body theory; quantum Hall effect
81U20 \(S\)-matrix theory, etc. in quantum theory
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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