The scattering and bound states of the many-body systems, related to theshort-range Dyson model, are studied. First, we show that the scattering statescan be realized as coherent states and the scattering Hamiltonian can beconnected to a free system. Unlike the closely related Calogero-Moser model,only a part of the partial waves acquire energy independent phase shifts, afterscattering. The cause of the same is traced to the reduction in thedegeneracies. The bound state Hamiltonian for the full-line problem is alsostudied and the relationship of its Hilbert space with that of the decoupledoscillators elucidated. Finally, we analyze the related models on circle andconstruct a part of the excitation spectrum through symmetry arguments.
展开▼
