Graduate Wigner Weisskopf method for time varying Perturbation

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The Wigner Weisskopf method is utilized in Time Dependent Perturbation Theory to analyze the transition from an initial state to final states under a constant step potential perturbation. However, many physical scenarios, such as photoionization, involve time-varying perturbations like harmonic or exponential ones. The discussion centers on whether this method can be adapted for such time-dependent cases and what resources exist that explore this adaptation, particularly regarding line width and wavefunction evolution. Participants highlight the need to incorporate the temporal aspect of the Hamiltonian into the Wigner Weisskopf approximation for time-varying perturbations. Overall, the conversation seeks clarity on the applicability of the Wigner Weisskopf method to time-varying perturbations and relevant literature on the subject.
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Is it possible to use the Wigner Weisskopf method for transitions from a discrete state to a continuum in the case of a time varying perturbation.
In Time Dependent Perturbation Theory for coupling of a discrete state to a continuum you use the Wigner Weisskopf method to describe how the initial state gets depopulated and final states populated and the line shape for the case of a constant step potential perturbation. However many cases of coupling to a continuum like photoionization aren’t described by a constant perturbation rather a harmonic one. Can this method be extended to a time varying perturbation for example harmonic or exponential. If so are there any sources books, lecture notes, and papers which discuss Wigner Weisskopf method for time varying perturbations for example the line width and wavefunction evolution for a continuum transition in the case of a time varying perturbation say a sinusoidal one for photoionization. Presumably you would just insert into the integral when applying the Wigner Weisskopf approximation the temporal part of the Hamiltonian the same way you do for a constant perturbation, if so are there any sources which discuss this to make sure this is the correct approach. Also does this method even work for time varying Perturbations.
 
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No, it's for the harmonically time-dependent perturbation. The photon fields are time-dependent!
 

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