Abstract
A method for Einstein-Brillouin-Keller (EBK) semiclassical wave functions is applied to the case where the quantizing torus is close to a chain of resonance islands, and standard EBK wave functions are distorted by the resonance islands. The method tested here is a modification of a recent “direct trajectory” implementation of the standard EBK method. The phase factor of the semiclassical wave function is obtained exactly as by Yang and Kellman [Phys. Rev. A 62, 022105 (2000); 65, 034103 (2002)], by running a single trajectory on the quantizing torus. However, rather than obtaining the amplitude factor from this trajectory, the method here uses an ensemble of trajectories uniformly distributed in a region enclosing an area ħ around the torus. The agreement between the resulting semiclassical wave function and the quantum wave function is excellent.
- Received 19 December 2001
DOI:https://doi.org/10.1103/PhysRevA.65.064101
©2002 American Physical Society