Multichannel scattering problem with a nonseparable angular part as a boundary-value problem.

Abstract

We have developed an efficient computational method for solving the quantum multichannel scattering problem with a nonseparable angular part. The use of the nondirect product discrete-variable representation, suggested and developed by V. Melezhik, gives us an accurate approximation for the angular part of the desired wave function and, eventually, for the scattering parameters. Subsequent reduction of the problem to the boundary-value problem with well-defined block-band matrix of equation coefficients permits us to use efficient standard algorithms for its solution. We demonstrate the numerical efficiency, flexibility, and good convergence of the computational scheme in a quantitative description of the Feshbach resonances in pair collisions occurring in atomic traps and the scattering in strongly anisotropic traps. The method can also be used for the investigation of further actual problems in quantum physics. A natural extension is a description of spin-orbit coupling, intensively investigated in ultracold gases, and dipolar confinement-induced resonances.