Gamow-Siegert functions and Darboux-deformed short range potentials

TL;DR

This paper introduces a method to construct exactly solvable short-range potentials using Gamow-Siegert functions, leading to new Hermitian and non-Hermitian models with applications in wave refraction and absorption.

Contribution

It presents a novel approach to Darboux-deform potentials via resonance states, expanding the class of exactly solvable models in quantum mechanics.

Findings

Complex potentials act as optical devices that refract and absorb waves.

Resonance levels are accurately calculated for long lifetime states.

The method applies to square wells and barriers, producing superpositions of Fock-Breit-Wigner distributions.

Abstract

Darboux-deformations of short range one-dimensional potentials are constructed by means of Gamow-Siegert functions (resonance states). Results include both Hermitian and non-Hermitian short range potentials which are exactly solvable. As illustration, the method is applied to square wells and barriers for which the transmission coefficient is a superposition of Fock-Breit-Wigner distributions. Resonance levels are calculated in the long lifetime limit by means of analytical and numerical approaches. The new complex potentials behave as an optical device which both refracts and absorbs light waves.