Convergence and completeness for square-well Stark resonant state expansions

Abstract

In this paper, we investigate the completeness of the Stark resonant states for a particle in a square-well potential. We find that the resonant state expansions for target functions converge inside the potential well and that the existence of this convergence does not depend on the depth of the potential well, <i>V</i>₀. By analyzing the asymptotic form of the terms in these expansions, we prove some results on the relation between smoothness of target functions and the asymptotic rate of convergence of the corresponding resonant state expansion and show that the asymptotic rate of convergence is also independent of <i>V</i>₀, but the absolute size terms in the series asymptotically goes as <i>V</i>⁻¹₀.