Journal article

Approximate solutions to Mathieu's equation

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

PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES | ELSEVIER SCIENCE BV | Published : 2018

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.

University of Melbourne Researchers

Grants

Awarded by Australian Research Council under the Discovery and Centre of Excellence funding schemes


Funding Acknowledgements

This work was supported in part by the Australian Research Council under the Discovery and Centre of Excellence funding schemes (project numbers DP140100375 and CE170100039). Computational resources were provided by the NCI National Facility systems at the Australian National University through the National Computational Merit Allocation Scheme supported by the Australian Government.