On the relaxation to quantum-statistical equilibrium of the Wigner-Weisskopf atom in a one-dimensional radiation field. IV. Exact solution for finite systems

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Abstract
A full study, both analytic and numerical, is made of an exact solution, given in a previous paper of the series, for the problem of the spontaneous emission of a Wigner‐Weisskopf atom in a one‐dimensional radiation field, when the system is considered to be finite in extent. The solution is obtained directly from the Schrödinger equation of the problem. The numerical solution and results are compared extensively with two separate weak‐coupling approximations, treated earlier in the series, which were derived respectively from the Prigogine‐Résibois master equation and from the solution of the Schrödinger equation. It is found that the latter corresponds much better, except for exceedingly small systems, with the exact results, and that it accordingly takes better account of the effects due to the nonanalyticity of the solution when the coupling tends to zero. Some proposals are made for the general exploitation in nonequilibrium statistical mechanics of this feature, and also for a possible application to the study of radiationless transitions in molecules.