Quantum Scattering Theory in a Discrete Representation

Abstract

The approach to solving few-body scattering problems in a discrete representation of the stationary wave packets is described briefly. By projecting into the wave-packet basis, all the operators and wave functions are represented with finite matrices and vectors, so that the integral equations of scattering theory are reduced to their matrix analogs. In such a discrete representation, it is easy to construct the matrix analogs for any complicated operators such as total resolvent and also effective interactions between composite particles. Using a special spectral shift function formalism, multichannel scattering problem can be solved in a discrete representation without any scattering equations at all. The approach is illustrated by examples of multichannel and three-body scattering.