Time-dependent perturbation theory

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Time-dependent perturbation theory allows for the description of a quantum system's wavefunction as a linear combination of unperturbed eigenstates, even when the perturbation affects energy levels. The coefficients in this combination represent probability amplitudes, indicating the likelihood of finding the particle in various states, though the system is not in a definite energy eigenstate. Transition rates between states can be calculated, particularly in scenarios like an electron in an atom interacting with an oscillating electromagnetic field. The new, perturbed eigenfunctions are indeed superpositions of the old eigenfunctions and evolve over time, reflecting changes in the system. This framework is crucial for understanding quantum behavior in dynamic environments, such as those involving external fields.
  • #31
Niles said:
...Why is it always that is says a small time-dependent perturbation?

Actually the external force or field can be strong, not small. The time-dependent solution exists and can still be represented as a superposition of old basis vectors with time-dependent coefficients.

In case of small perturbation these exact coefficients are well approximated with the perturbation series (a la Taylor series). The perturbation theory technique is developing these coefficients in Taylor series in powers of perturbation. Thus smallness of V(t) guarantees good accuracy of a truncated series (practical convergence).
 

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