Long-term solutions in semiclassical radiation theory
C. R. Stroud, Jr. and E. T. Jaynes
Phys. Rev. A 1, 106 (1970).
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An improved form of semiclassical radiation theory is developed which
includes the effect of the atom's radiation field back on the atom. This
formalism is applied to the problem of a single "two-level atom"
interacting with a monochromatic field. The resulting equations are solved
without resorting to time-dependent perturbation theory, and are found to
predict the behaviour of the system over times long compared with the
lifetime for spontaneous transitions. Not only stimulated emission and
absorption, but also spontaneous emission with the proper Einstein A
coefficient, and a frequency shift which agrees at least semiquantitatively
with the Lamb shift are described. In addition, several nonlinear effects
involving the interference between spontaneous and stimulated radiation are
described, and new experiments which might detect such effects are
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