Calculus of Variations and Geometric Measure Theory

A. Figalli - C. Klein - P. Markovich - C. Sparber

WKB analysis of Bohmian dynamics

created by figalli on 24 Jan 2013


Accepted Paper

Inserted: 24 jan 2013
Last Updated: 24 jan 2013

Journal: Comm. Pure Appl. Math.
Year: 2013


We consider a semi-classically scaled Schrodinger equation with WKB initial data. We prove that in the classical limit the corresponding Bohmian trajectories converge (locally in measure) to the classical trajectories before the appearance of the first caustic. In a second step we show that after caustic onset this convergence in general no longer holds. In addition, we provide numerical simulations of the Bohmian trajectories in the semiclassical regime which illustrate the above results.