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arXiv · 2108.11077

The Anisotropic Gaussian Semi-Classical Schr\"{o}dinger Propagator

Panos D. Karageorge·George N. Makrakis
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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.

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Panos D. Karageorge, George N. Makrakis. 2021-08-25. The Anisotropic Gaussian Semi-Classical Schr\"{o}dinger Propagator. https://arxiv.org/abs/2108.11077

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