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The Asymptotics of the Gap in the Mathieu Equation

Avron, Joseph and Simon, Barry (1981) The Asymptotics of the Gap in the Mathieu Equation. Annals of Physics, 134 (1). pp. 76-84. ISSN 0003-4916. https://resolver.caltech.edu/CaltechAUTHORS:20180521-145909947

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Abstract

We provide a simple proof that the kth gap, Δ_k, for the Mathieu operator −d^2dx^2 + 2κcos(2x) is Δ_k = 8(κ4)^k[(k − 1)!]^(−2)(1 + o(k^(−2))), a result obtained (up to the value of an integral) by Harrell. The key observation is that what is involved is tunneling in momentum space.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/0003-4916(81)90005-1DOIArticle
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 1981 Published by Elsevier. Received November 20, 1980. Research partially supported by NSF Grant MCS-78-01885. Simon would like to thank the Sherman Fairchild Visiting Scholar Program for its support.
Funders:
Funding AgencyGrant Number
NSFMCS-78-01885
Sherman Fairchild FoundationUNSPECIFIED
Issue or Number:1
Record Number:CaltechAUTHORS:20180521-145909947
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180521-145909947
Official Citation:Joseph Avron, Barry Simon, The asymptotics of the gap in the Mathieu equation, Annals of Physics, Volume 134, Issue 1, 1981, Pages 76-84, ISSN 0003-4916, https://doi.org/10.1016/0003-4916(81)90005-1. (http://www.sciencedirect.com/science/article/pii/0003491681900051)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86521
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:21 May 2018 22:23
Last Modified:03 Oct 2019 19:44

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