Quantum monodromy and Bohr-Sommerfeld rules

Letters in Mathematical Physics

Volumn 55, Issue 3, 2001, Pages 205-217

  San, Vũ Ngoc ^a  

^a INSTITUT FOURIER   (France)

Author keywords

Bohr Sommerfeld rules; Completely integrable systems; Monodromy; Semiclassical quantisation

Indexed keywords

EID: 0041814705     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1010944312712     Document Type: Article

References (13)

1. Child, M. S.: Quantum states in a champagne bottle, J. Phys. A 31 (1998), 657-670.
2. 2O and other systems: new insight into the level structure of quasi-linear molecules, Molec. Phys. 96(3) (1999), 371-379.
3. Colin de Verdière, Y. and Parisse, B.: Équilibre instable en régime semi-classique I: Concentration microlocale, Comm. Partial Differential Equations 19(9-10) (1994), 1535-1563.
4. Cushman, R. and Duistermaat, J. J.: The quantum spherical pendulum, Bull. Amer. Math. Soc. (N.S.) 19 (1988), 475-479.
5. Cushman, R. and Sadovskií, D. A.: Monodromy in perturbed Kepler systems: hydrogen atom in crossed fields, Europhys. Lett. 47 (1999), 1-7.
6. Duistermaat, J. J.: On global action-angle variables, Comm. Pure App. Math 33 (1980), 687-706.
7. Faure, F. and Zhilinskií, B. I.: Topological chern indices in molecular spectra, Phys. Rev. Lett. 85 (2000), 960-963; quant-ph/9912091.
8. Guillemin, V. and Uribe, A.: Monodromy in the quantum spherical pendulum, Comm. Math. Phys. 122 (1989), 563-574.
9. Hörmander, L.: The Analysis of Linear Partial Differential Operators, volumes I-IV, Springer, New York, 1983-1990.
10. Kozin, I. N. and Roberts, R. M.: Monodromy in the spectrum of an axisymmetric top molecule in electric field, Preprint, Warwick Univ., 2000.
11. Sadovskií, D. A. and Zhilinskií, B. I.: Monodromy, diabolic points, and angular momentum coupling, Phys. Lett. A 256(4) (1999), 235-244.
12. Vũ Ngoc, S.: Quantum monodromy in integrable systems, Comm. Math. Phys. 203(2) (1999), 465-479.
13. Vũ Ngoc, S.: Bohr-Sommerfeld conditions for integrable systems with critical manifolds of focus-focus type, Comm. Pure Appl. Math. 53(2) (2000), 143-217.