Wigner Weisskopf method for time varying Perturbation

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Discussion Overview

The discussion revolves around the application of the Wigner Weisskopf method in Time Dependent Perturbation Theory, specifically regarding its extension to time varying perturbations such as harmonic or exponential forms. Participants explore whether this method can be adapted for scenarios like photoionization, which do not conform to a constant perturbation model.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about the possibility of extending the Wigner Weisskopf method to time varying perturbations, questioning if the method can be applied to harmonic perturbations in the context of photoionization.
  • Another participant provides links to resources that discuss the Wigner Weisskopf method, but notes that these resources primarily address constant perturbations.
  • A subsequent reply clarifies that the method can indeed apply to harmonically time-dependent perturbations, emphasizing that photon fields are inherently time-dependent.

Areas of Agreement / Disagreement

There appears to be some disagreement regarding the applicability of the Wigner Weisskopf method to time varying perturbations, with differing interpretations of the resources shared. The discussion remains unresolved as participants explore these different perspectives.

Contextual Notes

Participants express uncertainty about the correct approach to integrating time varying components into the Wigner Weisskopf approximation, and the discussion highlights a lack of consensus on the method's effectiveness for such perturbations.

masteralien
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TL;DR
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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