Globally Uniform Semiclassical Expressions for Time-Independent Wave Functions

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Abstract
A semiclassical approximation is presented which describes the time-independent wave function as an integral over the Lagrangian manifold associated with the state. The function produced is free of caustic singularities and satisfies the Schrödinger equation with an error that vanishes everywhere uniformly in the classical limit. Illustrative calculations are presented for one-dimensional systems.