Classical theory of radiative transitions

Shrodinger's original conception of the connection between the electric field and the wave function ψ is reinterpreted and extended. The new semiclassical approach to radiative transitions is based on the exact (not perturbative) description of a particle undergoing a transition between two energy eigenstates

The physical existence of such a wave function during a transition allows for a simple classical explanation of the origin of radiation from quantum mechanical systems, both in the usual bound state cases and in some new free particle transitions for which there have been no previous semiclassical accounts. The Compton effect, perhaps the phenomenon most frequently cited as evidence of the quantum nature of radiation, is thus given a classical explanation which yields the Klein-Nishina cross section and demonstrates the classical origin of photon-like behavior of the incident and scattered radiation.

Further confirmation of the classical nature of the electromagnetic field at the quantum mechanical level is presented in a new derivation of the Lamb shift, another famous phenomenon whose only acceptable explanation has been quantum electrodynamical. The calculated value of the 2P, 2S. shift in hydrogen is

V. = 1110 MHz ,

in good agreement with experiment (1057 MHz).

iv

A more complete discussion of the c1(t) and c2(t) transition coefficients is also carried out, leading finally to new semiclassical treatments of spontaneous emission and the blackbody spectrum. These two subjects have again long been believed to be explainable only by quantum electrodynamics.