Asymptotics for the Phase Space Schr\"{o}dinger Equation
Mathematical Physics
2020-05-19 v1 math.MP
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 .
Cite
@article{arxiv.2005.08558,
title = {Asymptotics for the Phase Space Schr\"{o}dinger Equation},
author = {P. D. Karageorge and G. N. Makrakis},
journal= {arXiv preprint arXiv:2005.08558},
year = {2020}
}