A Gauss Elimination Method for Resonances

TL;DR

This paper introduces a Gaussian elimination-based inverse iteration method within the complex coordinate approach to efficiently find real and complex resonance energies, providing a unified framework for various quantum problems.

Contribution

It presents a novel Gaussian elimination method for inverse iteration in the complex coordinate approach, unifying the calculation of bound and resonant states.

Findings

Effective in computing both real and complex energies

Provides a simple, uniform computational framework

Energy shift method aids in diagnostics

Abstract

A Gaussian elimination form of inverse iteration within the complex coordinate approach is shown to produce a simple uniform method of finding both real bound state energies and complex resonant state energies for several problems which have been treated by a variety of methods in the literature. The energy shift method for expectation values is shown to be a useful diagnostic tool.