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Physical Review Letters

Global, Uniform, Semiclassical Approximation to Wave Equations

John R. Klauder

Published Mar 3, 1986• 50 citations
Publisher

Abstract

The usual configuration-space semiclassical approximation to wave equations (e.g., Schr\"odinger's equation) needs refinement at caustics. When expressed in a phase-space coherent-state representation, such equations admit a semiclassical solution that properly captures the effects of caustics. Transformation of this expression to the configuration-space representation yields a global, uniform, semiclassical approximation.

DOI
10.1103/physrevlett.56.897

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The usual configuration-space semiclassical approximation to wave equations (e.g., Schr"odinger's equation) needs refinement at caustics. When expressed in a phase-space coherent-state representation, such equations admit a semiclassical solution that properly captures the effects of caustics. Transformation of this expression to the configuration-space representation yields a global, uniform, semiclassical approximation.
We present a new method for treating classical (or quantal) wave equations in the shortwavelength (semiclassical) regime, based on a description of the wave in the ray phase space. The coherent-state representation is defined, and the equation which it obeys is given and solved under assumptions similar to those of conventional eikonal theory. As indicated by an example, the result is a smooth distribution on phase space which, when "projected" onto configuration space, yields a wave field with no caustic singularities.