Exact Solutions for Many-Level Multiple-Resonance Problems

Abstract

The matrix elements of the time‐development operator are obtained exactly for the influence of many resonant or near‐resonant fields on a system with a finite number of levels for arbitrary initial conditions in a wide class of problems. Perturbative techniques are presented which enable the exact treatment of all perturbations to a desired order. As examples, a three‐level double‐resonance and two eight‐level triple‐resonance systems are given. The applications of these exact solutions to the treatment of perturbations, including relaxation phenomena, are presented using both standard‐perturbation‐theory and density‐matrix techniques.