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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Semiclassical resonance asymptotics for the delta potential on the half line
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by Kiril Datchev and Nkhalo Malawo PDF
Proc. Amer. Math. Soc. 150 (2022), 4909-4921 Request permission

Abstract:

We compute resonance width asymptotics for the delta potential on the half-line, by deriving a formula for resonances in terms of the Lambert W function and applying a series expansion. This potential is a simple model of a thin barrier, motivated by physical problems such as quantum corrals and leaky quantum graphs.
References
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Additional Information
  • Kiril Datchev
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-2067
  • MR Author ID: 860651
  • Email: kdatchev@purdue.edu
  • Nkhalo Malawo
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-2067
  • ORCID: 0000-0001-5594-0620
  • Email: nkhalom@protonmail.com
  • Received by editor(s): August 23, 2021
  • Received by editor(s) in revised form: January 4, 2022
  • Published electronically: June 16, 2022
  • Additional Notes: The first author was supported in part by NSF grant DMS-1708511. The second author was supported in part by an REU Grant from the Purdue Math Department Tong Endowment.
  • Communicated by: Tanya Christiansen
  • © Copyright 2022 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 150 (2022), 4909-4921
  • MSC (2020): Primary 81U24; Secondary 81Q20
  • DOI: https://doi.org/10.1090/proc/16001
  • MathSciNet review: 4489322