Gaussian beam methods for the Schrodinger equation in the semi-classical regime: Lagrangian and Eulerian formulations

Abstract

The solution to the Schrdinger equation is highly oscillatory when the rescaled Planck constant is small in the semiclassical regime. A direct numerical simulation requires the mesh size to be O(). The Gaussian beam method is an efficient way to solve the high frequency wave equations asymptotically, outperforming the geometric optics method in that the Gaussian beam method is accurate even at caustics.