Resonant-state expansion of the one-dimensional Schrödinger equation

Abstract

The resonant-state expansion (RSE), is a rigorous perturbative method recently developed in electrodynamics. This paper presents the RSE method applied to the one-dimensional Schrödinger equation. The method is used here to find the new spectrum of Eigen wavenumbers in a double-well system described by delta function potentials. The convergence of the RSE is tested with the available analytical solution for the triple well. RSE results are compared with the exact solutions for triple well. The method was demonstrated to be particularly suitable for calculating high-quality resonant states (RSs) and calculating their perturbations.