Classical Electrodynamics · Problem 16.1

Radiation Damping, Classical Models of Charged Particles — John David Jackson

Physics — E&M · radiation-damping-oscillator

Problem

A nonrelativistic particle of charge

e

and mass

m

is bound by a linear, isotropic, restoring force with force constant

m\omega_0^2

. Using (16.13) and (16.16) of Section 16.2, show that the energy and angular momentum of the particle both decrease exponentially from their initial values as

e^{-\Gamma t}

, where

\Gamma = \omega_0^2 \tau

. Quantum mechanically, the mean excitation energy of an oscillator decays in exactly the same way because the total radiative transition probability for a state with quantum numbers

n_0

l_0

\Gamma(n_0, l_0) = n_0 \Gamma

. The decay of the angular momentum approaches the classical law only for

l_0 \gg 1

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