OPTIMAL ERROR ESTIMATES FOR FIRST-ORDER GAUSSIAN BEAM APPROXIMATIONS TO THE SCHRÖDINGER EQUATION.

Gaussian beams are generally local asymptotic solutions to the linear wave equations in the high-frequency regime. Each Gaussian beam is concentrated around a specific ray path determined by the underlying Hamiltonian system. Expressed as some superposition of Gaussian beams, Gaussian beam approximation is expected to be a high-frequency asymptotic solution which remains globally valid even around caustics. We derive optimal first-order error estimates for firstorder Gaussian beam approximations, in both continuous and discrete levels, to the Schrodinger equation equipped with a WKB initial data. Our error estimates are valid for any spatial dimension and unaffected by the presence of caustics. Some numerical tests are presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]