Arbitrary trajectory quantization method - art. no. 016213

The arbitrary trajectory quantization method (ATQM) is a time dependent app roach to quasiclassical quantization based on the approximate dual relation ship 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 rei nvestigate the ATOM and show that at finite energies, a smoothened quasicla ssical kernel corresponds to the modified formula that includes CAP familie s while the delta function kernel corresponding to the periodic orbit formu la is recovered as E-->infinity. Several clarifications are also provided.