TY - JOUR

T1 - Analytical solution of the Sommerfeld–Page equation

AU - Silagadze, Zurab k.

PY - 2024/11/1

Y1 - 2024/11/1

N2 - The Sommerfeld–Page equation describes the non-relativistic dynamics of a classical electron modeled by a sphere of finite size with a uniform surface charge density. It is a delay differential equation, and almost no exact solution of this equation was known until recently. However, progress has been made, and an analytical solution was recently found for an almost identical delay differential equation, which arose in the context of the mathematical modeling of the COVID-19 epidemics. Inspired by this research, we offer a pedagogical exposition of how one can find an analytical solution of the Sommerfeld–Page equation.

AB - The Sommerfeld–Page equation describes the non-relativistic dynamics of a classical electron modeled by a sphere of finite size with a uniform surface charge density. It is a delay differential equation, and almost no exact solution of this equation was known until recently. However, progress has been made, and an analytical solution was recently found for an almost identical delay differential equation, which arose in the context of the mathematical modeling of the COVID-19 epidemics. Inspired by this research, we offer a pedagogical exposition of how one can find an analytical solution of the Sommerfeld–Page equation.

U2 - 10.1119/5.0156685

DO - 10.1119/5.0156685

M3 - Article

VL - 92

SP - 864

EP - 871

JO - American Journal of Physics

JF - American Journal of Physics

SN - 0002-9505

IS - 11

ER -