Applications of square-integrable basis functions for scattering problems: A comparison between approaches based on Toeplitz matrices and negative imaginary potentials.

Abstract

In this work are considered two quantum-mechanical approaches to treat a single-coordinate (Eckart-type) potential scattering process. The one approach is based on the application of Toeplitz matrices and the other on the application of negative imaginary (absorbing) potentials. It was found that for this type of ``reactive'' process, the method based on the Toeplitz matrices performed better.