Title: All Decks / ETH_Sem6_old / QMII / Chapter01

Q: Perturbation theory notation:
A: Actual problem
Perturbation Hamiltonian
Known Hamiltonian
Decomposition of actual problem:

Perturbation Theory Problem up to order 3:

Non-degenerate Perturbation theory: First order energy and state correction

Orthogonality and normalisation in perturbation theory

Non-degenerate Perturbation theory: Second order energy correction

Variational method central equation:

Integral form of SE:

Integral solution to TDSE:

Definition Time Ordering Opperator:

Integral solution to TDSE (with time ordering op)

Interaction picture transformations:

Interaction picture perturbation theory

Q: Transition amplitude:
A: Probability of finding an initial state \(i\) transformed to \(f\) between \(t_0 \) and \(t\)
First order:

Fermis golden rule:

Q: Approximations FGR:
A: \(\Gamma_i = const\) for \(t \gg \Delta t\). Transition needs to be quick relative to transition rate. \(\Delta t <^! 1/\Gamma_i\)
(Due to getting larger than 1 transition probability elswise)