Wigner Weisskopf method for time varying Perturbation

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In summary, the Wigner-Weisskopf method is a theoretical approach used to analyze time-dependent perturbations in quantum mechanics. It focuses on the transition of quantum states under the influence of a weak external perturbation, allowing for the calculation of transition rates and probabilities. The method employs perturbation theory to derive an effective Hamiltonian that accounts for the interaction between the system and the perturbation over time. This technique is particularly useful in understanding phenomena such as spontaneous emission and the dynamics of quantum systems influenced by external fields.
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masteralien
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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!
 

FAQ: Wigner Weisskopf method for time varying Perturbation

What is the Wigner-Weisskopf method?

The Wigner-Weisskopf method is a theoretical approach used in quantum mechanics to describe the time evolution of a quantum system under the influence of a time-dependent perturbation. It is particularly useful for studying the decay processes and the interaction of atoms with electromagnetic fields.

How does the Wigner-Weisskopf method apply to time-varying perturbations?

The Wigner-Weisskopf method can be extended to handle time-varying perturbations by considering the time-dependent Schrödinger equation. The method involves expanding the state vector in terms of the unperturbed eigenstates and then solving the resulting set of coupled differential equations to find the time evolution of the system.

What are the main assumptions of the Wigner-Weisskopf method?

The main assumptions of the Wigner-Weisskopf method include: (1) the perturbation is weak compared to the unperturbed Hamiltonian, (2) the system starts in a well-defined initial state, and (3) the perturbation can be treated using first-order time-dependent perturbation theory. These assumptions simplify the mathematical treatment and make the method applicable to a wide range of physical systems.

What are some common applications of the Wigner-Weisskopf method?

The Wigner-Weisskopf method is commonly used in quantum optics to describe the spontaneous emission of photons by excited atoms, in nuclear physics to study radioactive decay, and in solid-state physics to analyze the interaction of electrons with phonons or other quasiparticles. It provides a framework for understanding the decay rates and transition probabilities in these systems.

What are the limitations of the Wigner-Weisskopf method?

While the Wigner-Weisskopf method is powerful, it has limitations. It assumes that the perturbation is weak and that higher-order effects can be neglected. It also may not accurately describe systems with strong interactions or non-Markovian dynamics, where the memory effects play a significant role. Additionally, the method is less effective for systems with complex time-dependent perturbations that cannot be easily handled within the first-order perturbation theory.

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