Many Body Problems with "Spin"-Related Contact Interactions

Abstract

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.

13 pages, Latex

References in corpus (2)

• Many-body system with a four-parameter family of point interactions in one dimension
• Gauge fields, point interactions and few-body problems in one dimension

Cited by in corpus (6)

• Trigonometric Cherednik algebra at critical level and quantum many-body problems
• Exactly Solvable Many-Body Systems and Pseudo-Hermitian Point Interactions
• Integrability and PT-symmetry of $N$-Body Systems with Spin-coupling $\delta$-Interactions
• On Integrability and Pseudo-Hermitian Systems with Spin-Coupling Point Interactions
• Spectrum of a family of spin-orbit coupled Hamiltonians with singular perturbation
• Random Hamiltonians with Arbitrary Point Interactions