Published June 1981
| public
Journal Article
The Asymptotics of the Gap in the Mathieu Equation
- Creators
- Avron, Joseph
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Simon, Barry
Chicago
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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.
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.Additional details
- Eprint ID
- 86521
- Resolver ID
- CaltechAUTHORS:20180521-145909947
- NSF
- MCS-78-01885
- Sherman Fairchild Foundation
- Created
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2018-05-21Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field