False singularities in partial sums over closed orbits
- 1 December 1987
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 20 (17) , L1139-L1141
- https://doi.org/10.1088/0305-4470/20/17/002
Abstract
The contribution to the spectral density from all the repetitions of a single classical closed orbit can have singularities that are not eigenenergies of the system. Only by summing over all different topologies of orbits do these false singularities get replaced by delta peaks at the true eigenenergies. The authors illustrate this with an example where the expansion and sum over repetitions are exact rather than asymptotic.Keywords
This publication has 6 references indexed in Scilit:
- Closed orbits and the regular bound spectrumProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1976
- Distribution of eigenfrequencies for the wave equation in a finite domain: III. Eigenfrequency density oscillationsAnnals of Physics, 1972
- Periodic Orbits and Classical Quantization ConditionsJournal of Mathematical Physics, 1971
- Energy Spectrum According to Classical MechanicsJournal of Mathematical Physics, 1970
- Phase-Integral Approximation in Momentum Space and the Bound States of an Atom. IIJournal of Mathematical Physics, 1969
- Phase-Integral Approximation in Momentum Space and the Bound States of an AtomJournal of Mathematical Physics, 1967