TY - JOUR

T1 - Approximate solutions to Mathieu's equation

AU - Wilkinson, Samuel A.

AU - Vogt, Nicolas

AU - Golubev, Dmitry S.

AU - Cole, Jared H.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85042694312&partnerID=8YFLogxK

U2 - 10.1016/j.physe.2018.02.019

DO - 10.1016/j.physe.2018.02.019

M3 - Article

AN - SCOPUS:85042694312

SN - 1386-9477

VL - 100

SP - 24

EP - 30

JO - Physica E: Low-Dimensional Systems and Nanostructures

JF - Physica E: Low-Dimensional Systems and Nanostructures

ER -