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Convergence and completeness for square-well Stark resonant state expansions

Permanent link
https://hdl.handle.net/10037/22583
DOI
https://doi.org/10.1063/1.5042523
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Date
2018-11-02
Type
Journal article
Tidsskriftartikkel
Peer reviewed

Author
Juhász, David; Kolesik, Miro; Jakobsen, Per
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, V0. 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 V0, but the absolute size terms in the series asymptotically goes as V−10.
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This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.
Is part of
Juhász, D. (2021). Nonlinear optics. (Doctoral thesis). https://hdl.handle.net/10037/22578.
Publisher
AIP Publishing
Citation
Juhász, D., Kolesik, M. & Jakobsen, P.K. (2018). Convergence and completeness for square-well Stark resonant state expansions. Journal of Mathematical Physics, 59(11), 113501.
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  • Artikler, rapporter og annet (matematikk og statistikk) [354]
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