Symplectic Semiclassical Wave Packet Dynamics II: Non-Gaussian States

TL;DR

This paper extends the symplectic semiclassical wave packet framework to include non-Gaussian states, deriving Hamiltonian systems and demonstrating accurate short-time dynamics approximation through numerical experiments.

Contribution

It introduces a generalized symplectic formulation for non-Gaussian semiclassical wave packets, expanding the scope of prior Gaussian-focused models.

Findings

Hamiltonian systems for non-Gaussian wave packets derived

Asymptotic expansions of associated Hamiltonians obtained

Numerical results show good short-time approximation accuracy

Abstract

We generalize our earlier work on the symplectic/Hamiltonian formulation of the dynamics of the Gaussian wave packet to non-Gaussian semiclassical wave packets. We find the symplectic forms and asymptotic expansions of the Hamiltonians associated with these semiclassical wave packets, and obtain Hamiltonian systems governing their dynamics. Numerical experiments demonstrate that the dynamics give a very good approximation to the short-time dynamics of the expectation values computed by a method based on Egorov's Theorem or the Initial Value Representation.