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arXiv · 2005.08558

Asymptotics for the Phase Space Schr\"{o}dinger Equation

P. D. Karageorge·G. N. Makrakis
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Abstract

We consider semi-classical time evolution for the phase space Schr\"{o}dinger equation. We construct a semi-classical phase space propagator in terms of semi-classical wave packets by the Anisotropic Gaussian Approximation, related to the Nearby Orbit Approximation. We deduce the canonical system in double phase space, related to the Berezin-Shubin-Marinov canonical system and construct a semi-classical asymptotic solution of the Cauchy problem for the phase space Schr\"{o}dinger equation for initial WKB states. We illustrate the method for sub-quadratic potentials in $\mathbb{R}$.

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P. D. Karageorge, G. N. Makrakis. 2020-05-18. Asymptotics for the Phase Space Schr\"{o}dinger Equation. https://arxiv.org/abs/2005.08558

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