"Jarring" of a quantum system and the corresponding stimulated transitions

Abstract

A systematic theory of sudden perturbations is derived for quantum systems whose states are described both by wave functions (a pure ensemble) and by a quantum density operator (a mixed ensemble). A perturbation series is written in powers of the parameter ωτ, which is small when the perturbation is sudden; ω is the typical eigenvalue of the unperturbed system; and τ is the characteristic collision time. When the perturbation (t), taken at different times, commutes with itself, the theory yields a compact analytic expression for the probabilities for stimulated transitions for any value of Vτ /. The results of many cross-section calculations for atomic collision processes are discussed from a common standpoint: the processes are treated as jarring processes which stimulate transitions in the quantum system. If a momentum δp is rapidly transferred to the system in a collision, regardless of the physical nature of the jarring, the probabilities for the stimulated transitions are governed by the parameter N ~δpδR/ where δR is a measure of the uncertainty in the coordinates which is due to the relatively slow motions in the unperturbed system.