PHASE-SPACE DYNAMICS AND QUANTUM-MECHANICS

An n-dimensional system with a classical Hamiltonian H(p, q, t) may be described by a phase-space distribution function D(q, p, t). The dynamical equation for D(q, p, t) is postulated to be {Mathematical expression} where σt is small and the phase angle 2πS/h is defined by {Mathematical expression} with {Mathematical expression} The dynamical equation follows from a simple conceptual picture for propagation of the distribution function in phase space. This equation leads to (1) solutions of the form D(q, p, t)=h-n/2 φ* (q, t)a(p t)ei2πq · p/h where φ(q, t) and a(p, t) are related as Fourier transforms, and (2) the time-dependent Schrödinger equation. © 1990 Springer-Verlag.