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In this paper we investigate the completeness of the Stark resonanteigenstates for a particle in a square-well potential. We find that theresonant state expansions for target functions converge inside the potentialwell and that the existence of this convergence does not depend on the depth ofthe potential well. By analyzing the asymptotic form of the terms in theseexpansions we prove some results on the relation between smoothness of targetfunctions and the rate of convergence of the corresponding resonant stateexpansion.

Convergence and completeness for square-well Stark resonant state expansions