Comparison of classical and quantal spectra for the Henon-Heiles potential
- 1 September 1981
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 14 (9) , L319-L327
- https://doi.org/10.1088/0305-4470/14/9/002
Abstract
The quantal energy spectrum is compared with the classical motion for a modified Henon-Heiles potential. There is good agreement between the amount of classical irregular motion and the proportion of energy eigenvalues sensitive to small changes in the perturbation parameter (as predicted by Percival (1973)). The work of Pomphrey (1974) and Noid et al. (1980) is extended by taking into account the full symmetry of the Hamiltonian when computing the eigenvalues, and by showing that most of the high second differences of energy eigenvalues as a function of perturbation parameter correspond to avoided crossings.Keywords
This publication has 9 references indexed in Scilit:
- Properties of vibrational energy levels in the quasi periodic and stochastic regimesThe Journal of Chemical Physics, 1980
- Regular and irregular semiclassical wavefunctionsJournal of Physics A: General Physics, 1977
- Semiclassical calculation of bound states in a multidimensional system for nearly 1:1 degenerate systemsThe Journal of Chemical Physics, 1977
- Numerical identification of regular and irregular spectraJournal of Physics B: Atomic and Molecular Physics, 1974
- Regular and irregular spectraJournal of Physics B: Atomic and Molecular Physics, 1973
- Orbits in Highly Perturbed Dynamical Systems. 111. Nonperiodic OrbitsThe Astronomical Journal, 1971
- The applicability of the third integral of motion: Some numerical experimentsThe Astronomical Journal, 1964
- Generalized orbital angular momentum and the n-fold degenerate quantum-mechanical oscillatorJournal of Molecular Spectroscopy, 1960
- The Crossing of Potential Surfaces.The Journal of Physical Chemistry, 1937