# Energy shifts in time dependent perturbation theory

• I
• Malamala
In summary, the AC Stark effect is used to modify the energy levels of an atom or molecule in the presence of an oscillating electric or magnetic field. The effect is based on the perturbative Hamiltonian and depends on the frequency of the field and the resonance frequency of the atom or molecule. To calculate the energy shift, we must solve the Schrodinger equation with the perturbative Hamiltonian.
Malamala
Hello! I saw in many papers people talking about the effects of a time dependent perturbation (usually an oscillating E or B field) on the energy levels of an atom or molecule (for now let's assume this is a 2 level system). Taking about energy makes sense when the hamiltonian is time independent. But here it is not. Moreover, this shift (e.g. AC Stark Shift) it's a constant (which depends on the magnitude and frequency of the field), even if the field itself is time varying. Given that this is usually talked about in the context of perturbation theory, I assume that at a point we do an approximation related to the relative frequencies of the field and of the atom (the resonance frequency), but I am not sure how to proceed. Can someone help me a bit in understanding this? Here is the paper that I am reading that made me ask this question. Thank you!

The paper you are reading is talking about a technique called the AC Stark effect, which is used to modify the energy levels of an atom or molecule in the presence of an oscillating electric or magnetic field. The AC Stark effect is based on perturbation theory and involves finding the energy shifts due to the external field. To do this, we must calculate the expectation value of the perturbative Hamiltonian for the system in the presence of the field. The perturbative Hamiltonian contains terms that depend on the frequency of the external field and the resonance frequency of the atom or molecule. If the field frequency is close to the resonance frequency of the atom or molecule, then the energy shift is significant. In order to calculate the energy shift, we need to solve the Schrodinger equation with the perturbative Hamiltonian. This is usually done using a perturbative expansion, where we expand the energy shifts in terms of the strength of the external field and the frequency of the field. We then use the energy shifts to modify the energy levels of the atom or molecule. Hope this helps!

## 1. What is time dependent perturbation theory?

Time dependent perturbation theory is a mathematical framework used in quantum mechanics to study the behavior of a quantum system when it is subjected to an external time-dependent perturbation. This theory allows us to calculate the probability of transitions between different energy levels of the system.

## 2. How does energy shift in time dependent perturbation theory?

In time dependent perturbation theory, the energy levels of a quantum system can shift due to the influence of an external perturbation. This shift is caused by the interaction between the system and the perturbation, and it can lead to changes in the probability of transitions between energy levels.

## 3. What are the applications of time dependent perturbation theory?

Time dependent perturbation theory has a wide range of applications in quantum mechanics, including the study of atomic and molecular spectra, quantum optics, and nuclear physics. It is also used in fields such as chemistry and materials science to understand the behavior of complex systems.

## 4. What are the limitations of time dependent perturbation theory?

One of the main limitations of time dependent perturbation theory is that it only applies to weak perturbations. If the perturbation is too strong, the theory may not accurately predict the behavior of the system. Additionally, this theory assumes that the perturbation is time-dependent, which may not always be the case.

## 5. How does time dependent perturbation theory relate to other perturbation theories?

Time dependent perturbation theory is a more general form of time-independent perturbation theory, which is used to study the behavior of a quantum system subjected to a static perturbation. Time dependent perturbation theory also has connections to other theories such as adiabatic perturbation theory and the rotating wave approximation, which are used in different contexts and under different assumptions.

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