FICTON THEORY OF DYNAMICAL SYSTEMS WITH NOISY PARAMETERS

Abstract

The theory of randomly perturbed waves described previously (Bourret 1962a, b) is presented in a form applicable to purely time-dependent systems, classical or quantum mechanical. It is then applied to the problem of a spin-[Formula: see text] dipole in a magnetic field with random fluctuations. One- and two-ficton processes are taken into account and a "renormalization" approximation is given also. Graphical comparison of the approximate solutions with the exact solution is presented. As a classical example, the harmonic oscillator with a noisy frequency parameter is analyzed in both the one- and two-ficton approximations.