# Resonant state expansion applied to one-dimensional quantum systems

## TL;DR

This paper adapts the resonant state expansion, a perturbation theory from electrodynamics, to one-dimensional quantum systems to accurately find resonant states in various potential configurations.

## Contribution

It introduces and verifies the application of the resonant state expansion to quantum systems, demonstrating its convergence and effectiveness in complex potential structures.

## Key findings

- Converges to analytic solutions for triple quantum wells
- Accurately characterizes resonant states in periodic potentials
- Validates the method's applicability to quantum systems

## Abstract

The resonant state expansion, a rigorous perturbation theory, recently developed in electrodynamics, is applied to non-relativistic quantum mechanical systems in one dimension. The method is used here for finding the resonant states in various potentials approximated by combinations of Dirac delta functions. The resonant state expansion is first verified for a triple quantum well system, showing convergence to the available analytic solution as the number of resonant states in the basis increases. The method is then applied to multiple quantum well and barrier structures, including finite periodic systems. Results are compared with the eigenstates in triple quantum wells and infinite periodic potentials, revealing the nature of the resonant states in the studied systems.