Analytical solution of the Sommerfeld–Page equation. / Silagadze, Zurab k.
In: American Journal of Physics, Vol. 92, No. 11, 01.11.2024, p. 864-871.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 60779268