Theory of Natural Line Shape
The initial state assumed for the system (atom in excited state with no photons present) seems quite unphysical. The state preparation and the dependence of the decay on the excitation should be discussed.
The Weisskopf-Wigner exponential decay “Ansatz” cannot be valid for all times. Deviations from it are expected to be extremely small for long-lived decaying states such as the atomic ones. However, the range of validity of the exponential decay law should be determined.
The state space was restricted to a two-level atom and to the vacuum and one-photon sectors, without any indication of how to proceed in order to improve the approximation. For such a basic problem, a clear-cut formulation should be provided, as well as a systematic procedure for deriving corrections to the Weisskopf-Wigner approximation.
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