A METHOD TO UNIFY CLASSIC AND QUANTUM DYNAMICS

Abstract

We descrioe a method that links Hilbert-space and phase-space operators. This procedure use Weyl's operator with complex parameters of position Q and momentum Pand a function S(Q, P, t) related with the classical action. The phase-space Hamiltonian of the system is expanded as a sum of differential operators depending of Planck's constant h. This allows to identify the leading quantum contribution and define a complex classical dynamics. In the limit h -+ O, the Schrodinger equation is transformed in a Liouville's equation for the phase-space wavefunction. The article ends with the application of the method to study the dynamics of a quartic oscillator.