J-matrix method of scattering for potentials with inverse square singularity: The real representation

TL;DR

This paper extends the J-matrix scattering method to handle potentials with inverse square singularities, improving its applicability to more complex quantum scattering problems.

Contribution

The paper introduces a real representation of the J-matrix method specifically designed for inverse square singular potentials, expanding its scope beyond short-range and 1/r singular potentials.

Findings

Enhanced accuracy and stability for inverse square singular potentials

Successful demonstration of the method's convergence

Broader applicability to quantum scattering problems

Abstract

The J-matrix method was developed to handle regular short-range scattering potentials. Its accuracy, stability, and convergence properties compare favorably with other successful scattering methods. Recently, we extended the method to the treatment of potentials with 1/r singularity. In this work, we do the same for 1/r^2 singular potentials.