Phase quantization of chaos and the role of the semiclassical amplitude factor

In a recent paper [Takatsuka, Takahashi, Koh and Yamashita, J. Chem. Phys. 126 (2007), 021104], it was shown that the semiclassical quantization of chaos can be accurately achieved only with the phases (the action and Maslov phases) without use of the amplitude (preexponential) factor, which is known to diverge exponentially in chaos. The aim of this paper is to analyze the role of the semiclassical amplitude in energy quantization from various points of view, and we actually show that it is indeed quite limited. Therefore even chaos is quantized mainly by the phase constructive and destructive interferences.