Bound State Semiclassical Wave Functions

The semiclassical theory developed by Maslov and Fedoriuk is used to calculate the wave function for a two‐dimensional bound state system. We investigate in detail an eigenstate of a coupled anharmonic oscillator system. The primitive semiclassical wave function is obtained from the characteristic function S and the density function J. Each of these functions consists of four branches corresponding to the four possible directions of motion of the classical trajectory through any point. The interference from the four branches determines the basic structure of the wave function. A uniform approximation gives a wave function which is well behaved along each caustic and which is in good agreement with the fully quantal wave function