Time-dependent perturbation theory is a method used in quantum mechanics to study the behavior of a system under the influence of a time-dependent external perturbation. It allows us to calculate the probability of transitions between different energy levels of a quantum system.
The main assumptions of time-dependent perturbation theory are that the perturbation is small compared to the unperturbed system and that the perturbation varies smoothly with time.
The time limit in time-dependent perturbation theory refers to the length of time for which the perturbation is applied to the system. This time limit is typically assumed to be finite, but in some cases, it can also be extended to an infinite time limit.
Time-dependent perturbation theory is used in many areas of physics, such as atomic and molecular physics, nuclear physics, and condensed matter physics. It is often used to study the dynamics of quantum systems and to calculate transition probabilities between energy levels.
Time-dependent perturbation theory is limited to systems with small perturbations and smooth time variations. It also assumes that the initial state of the system is known and that the perturbation is applied for a finite amount of time. In some cases, it may not accurately describe the behavior of a system, and more advanced methods may be needed.