Spherical pendulum, actions, and spin

Journal of Physical Chemistry

Volumn 100, Issue 49, 1996, Pages 19124-19135

  Richter, Peter H ^a   Dullin, Holger R ^a   Waalkens, Holger ^a   Wiersig, Jan ^a  

^a UNIVERSITY OF BREMEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002319766     PISSN: 00223654     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp9617128     Document Type: Article

References (22)

1. Born, M. Vorlesungen über Atommechanik; Springer: Berlin, 1925.
2. Einstein, A. Zum Quantensatz von Sommerfeld und Epstein. Verh. DPG 1917, 19, 82-92.
3. Berry, M. V. Some quantum-to-classical asymptotics. In Chaos and Quantum Physics; Giannoni et al., Eds.; Les Houches Summar School Lectures, Vol. 52; North Holland: Amsterdam, 1991; pp 251-303.
4. Heller, E. J. Wave packet dynamics and quantum chaology. In Chaos and Quantum Physics; Les Houches Summer School Lectures, Vol. 52; North Holland: Amsterdam, 1991; pp 547-663.
5. Gutzwiller, M. C. Chaos in Classical and Quantum Mechanics; Interdisciplinary Applied Mathematics; Springer: Berlin, 1990; Vol. 1.
6. Berry, M. V. Regular and irregular motion. In Topics in Nonlinear Dynamics; AIP Conference Proceedings, No. 46; American Institute of Physics: New York, 1978; pp 16-120.
7. Lichtenberg, A. J.; Lieberman, M. A. Regular and Chaotic Dynamics; Springer: Berlin, 1992.
8. Richter, P. H. Die Theorie des Kreisels in Bildern. Report 226, Institut für Dynamische Systeme, 1990.
9. Dullin, H. R. Die Energieflächen des Kowalewskaja-Kreisels; Mainz Verlag: Aachen, 1994; Dissertation.
10. Dullin, H. R.; Juhnke, M.; Richter, P. H. Action integrals and energy surfaces of the Kovalevskaya top. Bifurcation and Chaos 1994, 4(6), 1535-1562.
11. Richter, P. H.; Wittek, A.; Kharlamov, M. P.; Kharlamov, A. P. Action integrals for ellipsoidal billiards. Z. Naturforsch. 1995, 50a, 693-710.
12. Wiersig, J.; Richter, P. H. Energy surfaces of ellipsoidal billiards. Z. Naturforsch. 1996, 51a, 219-241.
13. Dullin, H. R.; Heudecker, O.; Juhnke, M.; Pleteit, H.; Schwebler, H.-P.; Waalkens, H.; Wiersig, J.; Wittek, A. Energy surfaces in action space; preprint, 1995.
14. Richter, P. H.; Dullin, H. R.; Wittek, A. Dynamics of the Spinning Top; Springer Verlag: Berlin, in press.
15. Bolsinov, A.; Dullin, H. R.; Wittek, A. Topology of energy surfaces and existence of transversal Poincaré sections. J. Phys. 1996, A29, 4977-4985.
16. Fomenko, A. T. Topological classification of all integrable Hamiltonian differential equations of general type with two degrees of freedom. In The Geometry of Hamiltonian Systems; T., Ratiu, Ed.; Springer: New York, 1991; pp 131-139.
17. Oshemkov, A. A. Fomenko invariants for the main integrable cases of the rigid body motion equations. In Topological Classification of Integrable Systems; Fomenko, A. T., Ed.; American Mathematical Society: Providence, RI, 1991.
18. Miller, W. H. Semiclassical treatment of multiple turning-point problems - phase shifts and eigenvalues. J. Chem. Phys. 1968, 48, 1651-1658.
19. Child, M. S. Semiclassical theory of tunneling and curve-crossing problems: a diagrammatic approach. J. Mol. Spectrosc. 1974, 53, 280-301.
20. Keller, J. B. Corrected Bohr-Sommerfeld quantum conditions for nonseparable systems. Ann. Phys. (NY) 1958, 4, 180-188.
21. Maslov, V. P. Théorie des Perturbations et Méthodes Asymptotiqites; Dunod: Paris, 1972.
22. Percival, Ian C. Semiclassical theory of bound states. Adv. Chem. Phys. 1977, 36, 1-61.