Direct trajectory method for semiclassical wave functions

This paper reports a method to build a semiclassical wave function corresponding to an invariant torus satisfying Einstein-Brillouin-Keller quantization conditions. Instead of calculating the stability matrix of the trajectory at each step, as in the standard method of Keller [Ann. Phys. (N.Y.) 4, 180 (1958)] or the modification of Maslov and Fedoriuk [Semiclassical Approximations in Quantum Mechanics (Reidel, Dordrecht, 1981)], we use the actual density of the trajectory, calculated by running the trajectory and counting passages through cells in coordinate space. The method is tested for a system of coupled Morse oscillators, and found to be comparable in accuracy to the standard method. It may be more useful than the standard method for testing ideas for semiclassical quantization in the chaotic regime.