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Published June 1981 | public
Journal Article

The Asymptotics of the Gap in the Mathieu Equation

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

Created:
August 19, 2023
Modified:
October 18, 2023