The Arbitrary Trajectory Quantization Method

Details The Arbitrary Trajectory Quantization Method The Arbitrary Trajectory Quantization Method

2001-07-12

arxiv.org/abs/nlin/0107024v1

Physical Review E Volume 63, 016213

Nonlinear Sciences

Chaotic Dynamics

revtex, ps figures

Scientific paper

10.1103/PhysRevE.63.016213

The arbitrary trajectory quantization method (ATQM) is a time dependent approach to quasiclassical quantization based on the approximate dual relationship that exists between the quantum energy spectra and classical periodic orbits. It has recently been shown however, that, for polygonal billiards, the periodicity criterion must be relaxed to include closed almost-periodic (CAP) orbit families in this relationship. In light of this result, we reinvestigate the ATQM and show that at finite energies, a smoothened quasiclassical kernel corresponds to the modified formula that includes CAP families while the delta function kernel corresponding to the periodic orbit formula is recovered at high energies. Several clarifications are also provided.

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