The Anisotropic Gaussian Semi-Classical Schr\"{o}dinger Propagator
Mathematical Physics
2021-08-26 v1 math.MP
Abstract
We present a construction of the Anisotropic Gaussian Semi-Classical Schr\"{o}dinger Propagator, emblematic of a class of Fourier Integral Operators of quadratic phase kernels related to the Schr\"{o}dinger equation. We deduce a set of algebraic relations of the variational matrices, solutions of the variational system pertaining to single Gaussian wave packet semi-classical time evolution, representing the symplectic and other invariances of the dynamics, which are subsequently used to derive the Van Vleck formula from the semi-classical propagator, as an argument for the practical importance of the later relations in the relevant wave packet calculus.
Keywords
Cite
@article{arxiv.2108.11077,
title = {The Anisotropic Gaussian Semi-Classical Schr\"{o}dinger Propagator},
author = {Panos D. Karageorge and George N. Makrakis},
journal= {arXiv preprint arXiv:2108.11077},
year = {2021}
}