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I have a problem understanding the essence of the lineshape function. This function is supposed to describe the linewidth of the emission from a two level system, i.e. practically, the discrete levels of stationary states are not exactly discrete. I thought this be the case when we include the interaction of the electromagnetic wave in the Hamiltonian of the problem. In other words, when we have an isolated atom, the states turn out to be stationary, there is no way for an electron to leave the stationary state if it already exists there as dictated by the time evolution of the wavefunction. In this case, the energy levels turn out to be discrete and everything is OK. I thought that when we include an electromagnetic wave of the correct frequency in the Hamiltonian of the problem, that is the system is no more isolated but interacting with radiation, we should be able to calculate the spread in the discrete energy levels due to the uncertainty principle directly from the Schrodinger equation. Unfortunately this does not turn out to be the case and we have to introduce this spread in an adhoc fashion. I have tried to look for a derivation from first principles to this problem, but I have failed. Does anybody know a solution?

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# Lineshape function

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