Approximate solutions to Mathieu's equation

Samuel A. Wilkinson*, Nicolas Vogt, Dmitry S. Golubev, Jared H. Cole

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

13 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)24-30
Number of pages7
JournalPhysica E: Low-Dimensional Systems and Nanostructures
Publication statusPublished - 1 Jun 2018
MoE publication typeA1 Journal article-refereed


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