Generalized semiclassical-phase-index formulas via sequential stationary phase

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 53, Issue 5, 1996, Pages 2958-2970

  Campolieti, G ^a   Brumer, Paul ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001479078     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.53.2958     Document Type: Article

References (15)

1. J. H. Van Vleck, Proc. Natl. Acad. Sci. U.S.A. 14, 178 (1928).
2. V. P. Maslov, USSR Comput. Math. Math. Phys. 3, 744 (1962).
3. M. Gutzwiller, Math. Phys. 8, 1979 (1967).
4. V. P. Maslov and M. V. Fedoryuk, Semiclassical Approximation in Quantum Mechanics (Reidel, Boston, 1981).
5. G. Campolieti and P. Brumer, Phys. Rev. A 50, 997 (1994).
6. M. V. Fedoryuk, USSR Comput. Math. Math. Phys. 2, 152 (1963).
7. J. N. L. Connor, Mol. Phys. 25, 181 (1973).
8. N. Bleistein and R. A. Handelsman, Asymptotic Expansions of Integrals (Dover, New York, 1986); A. Erdélyi, Asymptotic Expansions (Dover, New York, 1956).
9. Similar identities were employed by L. Hörmander, Acta Math. 127, 79 (1971).
10. D. Fujiwara, Nagoya Math. J. 124, 61 (1991).
11. W. H. Miller, Adv. Chem. Phys. 25, 69 (1974).
12. L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981).
13. H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, MA, 1980); V. I. Arnold, Mathematical Methods in Classical Mechanics (North-Holland, New York, 1980); E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, 4th ed. (Cambridge University Press, Cambridge, 1937).
14. See also S. Levit, K. Möhring, U. Smilansky and T. Dreyfus, Ann. Phys. (N.Y.) 114, 223 (1978).
15. See also the recent review of Maslov theory by R. G. Littlejohn, J. Stat. Phys. 68, 7 (1992).