Semiclassical eigenvalues for non-separable bound systems from classical trajectories: The degenerate case
- 1 November 1976
- journal article
- research article
- Published by Informa UK Limited in Molecular Physics
- Vol. 32 (5), 1327-1347
- https://doi.org/10.1080/00268977600102721
Abstract
Semiclassical quantum conditions for arbitrary non-separable systems are derived. These lead to energy eigenvalues in good agreement with quantum results for both degenerate and non-degenerate two-dimensional (2D) systems. The applicability of these quantization rules is related to the structure of the caustics of the motion.Keywords
This publication has 20 references indexed in Scilit:
- Semiclassical eigenvalues for nonseparable systems: Nonperturbative solution of the Hamilton–Jacobi equation in action-angle variablesThe Journal of Chemical Physics, 1976
- Vibrational quantization of polyatomic moleculesMolecular Physics, 1976
- Semiclassical calculation of bound states in a multidimensional system. Use of Poincaré’s surface of sectionThe Journal of Chemical Physics, 1975
- Semiclassical calculation of bound states of a multidimensional systemThe Journal of Chemical Physics, 1974
- Variational principles for the invariant toroids of classical dynamicsJournal of Physics A: Mathematical, Nuclear and General, 1974
- Regular and irregular spectraJournal of Physics B: Atomic and Molecular Physics, 1973
- Amplitude Instability and Ergodic Behavior for Conservative Nonlinear Oscillator SystemsPhysical Review B, 1969
- The applicability of the third integral of motion: Some numerical experimentsThe Astronomical Journal, 1964
- Resonance cases and small divisors in a third integral of motion. IThe Astronomical Journal, 1963
- Corrected bohr-sommerfeld quantum conditions for nonseparable systemsAnnals of Physics, 1958