Various theories that use the sudden jump model to explain the time dependence of the optical band of a single molecule in a fluctuating environment are analyzed. It is shown that the dynamic theory of the optical band, based on the Hamiltonian of the system, should necessarily include the initial conditions for the quantum system. We show how these initial conditions should be chosen for the dynamic theory to properly describe the quantum jumps of the optical band of a single molecule. Unlike stochastic theories based on the sudden jump model, the dynamic theory predicts several absorptances of a single molecule and directly connects the absorptance fluctuations with this fact. The theory is used to account for the time dependence of the broadening of experimentally measured lines of individual molecules.
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