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Journal of Physics A Mathematical and General

A solvable non-separable quantum two-body problem

M. L. Glasser

Published Sep 7, 1993• 6 citations
Publisher

Abstract

Presents a non-separable one-dimensional two-body problem. It describes the reflection of a two-particle bound state off a discontinuity across which there is a steplike change in the interparticle potential. The model can be used as a primitive description of a pick-up or stripping reaction at an interface and also describes the diffusion of a particle in a plane containing an extended finite depth trap. The reflection coefficient for the discontinuity is obtained in closed form.

DOI
10.1088/0305-4470/26/17/013

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Presents a non-separable one-dimensional two-body problem. It describes the reflection of a two-particle bound state off a discontinuity across which there is a steplike change in the interparticle potential. The model can be used as a primitive description of a pick-up or stripping reaction at an interface and also describes the diffusion of a particle in a plane containing an extended finite depth trap. The reflection coefficient for the discontinuity is obtained in closed form.
A one-particle non-relativistic quantum mechanical solvable model in two-dimensional space is given. The Hamiltonian is the sum of kinetic and interaction parts. Interactions are separable and can be centred at n arbitrary points of the plane. Conditions for the existence and for the number of bound states in finite linear chains are formulated in terms of the parameters of the interactions and intercentre distances. Scattering problems are also considered. Finally, when the interactions are centred in a single centre, it is shown that the model remains solvable in the presence of a uniform magnetic field of arbitrary intensity.
An exactly soluble one-dimensional three-body problem is presented, in which the interaction between the particles consists of local two-body potentials between each two particles. Infinitely high step functions are chosen for the form of the three potential functions. This interaction allows only three-body bound states and no continuum states. We have considered three different choices of the mass ratios of the three particles and we give formulas in closed form for the energies and for the wavefunctions of all states.
We consider bound and scattering states of the one-dimensional dimer formed by two coupled non-identical atoms when one of them also interacts with the zero-range potential located at the origin. By calculating the dimer localized and scattering wave functions, we identify properties of the system without the two-body bound-state breakdown. In general, we predict an enhancement of the dimer reflection compared to a single atom, except for a narrow region on the attractive side of the external potential.