Wigner Weisskopf method for time varying Perturbation

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SUMMARY

The Wigner Weisskopf method is utilized in Time Dependent Perturbation Theory to analyze the transition of discrete states to continuum states under constant perturbations. This discussion explores the extension of this method to time-varying perturbations, specifically harmonic and exponential types, particularly in the context of photoionization. Participants seek resources that address the application of the Wigner Weisskopf approximation for sinusoidal perturbations and inquire about the validity of this approach for time-varying scenarios. Relevant links to lecture notes and papers are provided for further exploration.

PREREQUISITES
  • Understanding of Time Dependent Perturbation Theory
  • Familiarity with the Wigner Weisskopf method
  • Knowledge of photoionization processes
  • Basic concepts of quantum mechanics and Hamiltonians
NEXT STEPS
  • Research the application of the Wigner Weisskopf method to harmonic perturbations in quantum mechanics
  • Study the effects of time-varying potentials on wavefunction evolution
  • Examine literature on photoionization and its relation to time-dependent perturbations
  • Explore advanced quantum mechanics textbooks that cover perturbation theory in depth
USEFUL FOR

Quantum physicists, researchers in atomic and molecular physics, and students studying advanced quantum mechanics who are interested in perturbation theory and its applications to time-varying systems.

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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