The hamilton formalism of gaussian wave-packet dynamics

Abstract

Gaussian wave packets have been used extensively to describe short-time localised processes in small molecular systems. We present a formalism to compute approximately the quantal time evolution of Gaussian wave packets for N-body systems. The wave-packet dynamics are obtained by invoking the time-dependent variational principle in Lagrangian form. It is then shown that the parametrisation of a Gaussian wave packet can be chosen so as to yield a Hamilton-like set of evolution equations for the wave-packet parameters. The resulting formalism proves to be energy conserving. For those parts of the system for which a classical description is appropriate, a localisation limit recovers the classical Hamilton equations. Also a mixed classical-quantal description of an N-body system is feasible.