Time, time-dependent perturbation theory, transitions

Steven M. Pascal

If the perturbation is turned on for a brief period of time and then turned off, the particle ends up in the original potential. But it may have been induced to transition from one eigenstate to another during the perturbation. The calculation of the probability of that transition is the topic of time-dependent perturbation theory (TDPT). Again, formula are presented rather than derived, and two examples are provided: a linear perturbation, and an oscillating perturbation. These examples, respectively, show how selection rules arise, and how light of a given frequency excites energy transitions of the same frequency. This latter phenomenon is called resonance .

T. Banks

Peter Joshua Atkins, Julio de Paula, Ronald Friedman

Contents Time-dependent perturbation theory 140 The general procedure 140 Example 16.1: Using time-dependent perturbation theory for a slowly switched perturbation 140 Oscillating perturbations and spectroscopic transitions 142 Example 16.2: Analysing spectroscopic transitions of a harmonic oscillator 142 The energy of time-varying...

Brian P. Anderson

E. V. Orlenko, Fedor E. Orlenko

A formalism Time-dependent Exchange Perturbation Theory (TDEPT) is built. A formula n-th term for arbitrary time dependency of perturbation is obtained. The formalism TDEPT is reduced to the standard form of invariant perturbation theory, taking into account the rearrangement of electrons between centers. A scattering S-matrix and T-matrix transitions are obtained in a general form for arbitrary interactions with respect to overlapping non-orthogonal states.