Asymptotic Approximations for the Phase Space Schrodinger Equation
Abstract
We consider semiclassical time evolution for the phase space Schrödinger equation and present two methods of constructing short time asymptotic solutions. The first method consists of constructing a semiclassical phase space propagator in terms of semiclassical Gaussian wave packets on the basis of the Anisotropic Gaussian Approximation, related to the Nearby Orbit Approximation, by which we derive an asymptotic solution for configuration space WKB initial data. The second method consists of constructing a phase space narrow beam asymptotic solution, following the Complex WKB Theory developed by Maslov, on the basis of a canonical system in double phase space related to the BerezinShubinMarinov HamiltonJacobi and transport equations. We illustrate the methods for subquadratic potentials in $\mathbb{R}$.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.11075
 Bibcode:
 2021arXiv210811075K
 Keywords:

 Mathematical Physics
 EPrint:
 arXiv admin note: substantial text overlap with arXiv:2005.08558