Shape of Specral Line At The Optical Decay of An Idealized Atom
The "isolated" quantum system (atom, ion, molecule or even a quantum dot) may have metastable states, weakly coupled to the outer world. (Some couliknd should be taken into account; otherwize, there is no optical decay.) In the idealized case, the evolution of the system is disturbed only by the interaction with the continuum of the modes of the electromagnetic field. Then, the spectral width of the emitted photons is determined by the relaxation rate. For the narrow spectral lines, the decay is almost exponential; then, the profile of the spectral line is determined by the Fourier-transform of the exponential decay of the quantum amplitude of probability that the system is still excited; this profile is Lorentian.
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