Semiclassical quantization of chaos in terms of an amplitude-free quasi-correlation function

A simple and practical semiclassical method based on an amplitude-free quasi-correlation function is proposed to quantize the energy spectrum of classically chaotic systems. Since classical trajectories used in this function are required to satisfy only a simple condition, the present method can be readily applied to a relatively large system. Numerical examples, which compare the semiclassical spectra with those of the full quantum mechanics in a two-dimensional system covering the regular and highly chaotic energy regions, show very clearly that the proposed amplitude-free quasi-correlation function can quantize chaos surprisingly well.