Approximate solutions to Mathieu's equation

Wilkinson, S, Vogt, N, Golubev, D and Cole, J 2018, 'Approximate solutions to Mathieu's equation', Physica E: Low-Dimensional Systems and Nanostructures, vol. 100, pp. 24-30.

Document type: Journal Article
Collection: Journal Articles

Title Approximate solutions to Mathieu's equation
Author(s) Wilkinson, S
Vogt, N
Golubev, D
Cole, J
Year 2018
Journal name Physica E: Low-Dimensional Systems and Nanostructures
Volume number 100
Start page 24
End page 30
Total pages 7
Publisher Elsevier BV North-Holland
Abstract Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.
Subject Electronic and Magnetic Properties of Condensed Matter; Superconductivity
DOI - identifier 10.1016/j.physe.2018.02.019
Copyright notice © 2018 Elsevier B.V. All rights reserved.
ISSN 1386-9477
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