Gaussian wave-packet dynamics: Semiquantal and semiclassical phase-space formalism

Gaussian wave packets are a popular tool for semiclassical analyses of classically chaotic systems. We demonstrate that they are extremely powerful in the semiquantal analysis of such systems, too, where their dynamics can be recast in an extended potential formulation. We develop Gaussian semiquantal dynamics to provide a phase-space formalism, and construct a propagator with desirable qualities. We qualitatively evaluate the behavior of these semiquantal equations, and show that they reproduce the quantal behavior better than the standard Gaussian semiclassical dynamics. We also show that these semiclassical equations arise as non-self-consistent (in ħ) truncations to semiquantal dynamics. This enables us to introduce an extended semiclassical dynamics that retains the power of the Hamiltonian phase-space formulation. Finally, we show how to obtain approximate eigenvalues and eigenfunctions in this formalism, and demonstrate with an example that this works well even for a classically strongly chaotic Hamiltonian.