Quantum dynamics in phase space: Moyal trajectories 3

Abstract

We present in this paper a new approach to the calculation of Moyal trajectories, which delivers straightforwardly the dynamical equations that determine these trajectories. We demonstrate this with three examples: the anharmonic oscillator with a Hamiltonian h(p, q) = p2/2 + q4/4, the physical pendulum with a Hamiltonian h(p,q)=p2/2+cos(q), and the Hènon-Heiles system with a Hamiltonian h(p1,p2,q1,q2)=(p12 + p22)/2 + (q12 + q22)/2 + q2(q12 − q22/3).