T-matrix in discrete oscillator representation

TL;DR

This paper analyzes the T-matrix in a discrete oscillator basis for bound and scattering states, focusing on a particle in a central potential and exploring how basis parameters influence the T-matrix expansion.

Contribution

It introduces a method to compute the T-matrix coefficients in a discrete oscillator basis for various potentials, highlighting dependence on basis parameters.

Findings

T-matrix coefficients vary with potential shape and basis parameters.

Derived linear equations for T-matrix expansion coefficients.

Analyzed four different potentials to demonstrate method applicability.

Abstract

We investigate T-matrix for bound and continuous-spectrum states in the discrete oscillator representation. The investigation is carried out for a model problem - the particle in the field of a central potential. A system of linear equations is derived to determine the coefficients of the T-matrix expansion in the oscillator functions. We selected four potentials (Gaussian, exponential, Yukawa, and square-well ones) to demonstrate peculiarities of the T-matrix and its dependence on the potential shape. We also study how the T-matrix expansion coefficients depend on the parameters of the oscillator basis such as the oscillator length and the number of basis functions involved in calculations.