Hamiltonian approach for the wave packet dynamics: Beyond Gaussian wave functions

TL;DR

This paper extends the Hamiltonian framework for wave packet dynamics to include non-Gaussian wave functions, enlarging the phase space while preserving Hamiltonian structure, and compares these methods for a quartic potential.

Contribution

It introduces generalized Hamiltonian approaches for non-Gaussian wave packets, expanding the theoretical framework beyond Gaussian functions.

Findings

Non-Gaussian extensions preserve Hamiltonian structure.

Comparison shows differences in wave packet evolution.

Framework applicable to complex potentials.

Abstract

It is well known that the Gaussian wave packet dynamics can be written in terms of Hamilton equations in the extended phase space that is twice as large as in the corresponding classical system. We construct several generalizations of this approach that include non-Gausssian wave packets. These generalizations lead to the further extension of the phase space while retaining the Hamilton structure of the equations of motion. We compare the Gaussian dynamics with these non-Gaussian extensions for a particle with the quartic potential.