Topological expansion and exponential asymptotics in 1D quantum mechanics

Journal of Physics A: Mathematical and General

Volumn 33, Issue 8, 2000, Pages 1543-1580

  Giller, Stefan ^a  

^a UNIVERSITY OF LODZ   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034598894     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/33/8/304     Document Type: Article

References (42)

1. Balian R and Bloch C 1974 Ann. Phys., NY 108 514
2. Giller S 1992 Acta Phys. Pol. B 23 457-511
3. Giller S and Milczarski P 1998 Borel summable solutions to Schrödinger equation Preprint quant-ph/9801031
4. Fröman N and Fröman P O 1965 JWKB Approximation. Contribution to the Theory (Amsterdam: North-Holland)
5. Graffi S, Grecchi V and Simon B 1970 Phys. Lett. B 32 631
6. Simon B and Dicke A 1970 Ann. Phys., NY 58 76
7. Bender C M and Wu T T 1969 Phys. Rev. 184 1231
8. Bender C M and Wu T T 1973 Phys. Rev. D 7 1620
9. Loeffel J J, Martin A, Simon B and Wightman A S 1969 Phys. Lett. B 30 656
10. Horzela A 1986 Acta Phys. Pol. B 17 425
11. Čizek J and Vrscay E R 1984 Phys. Rev. A 30 1550
12. Giller S 1989 J. Phys. A: Math. Gen. 22 2965
13. Giller S 1990 Acta Phys. Pol. B 21 675-709
14. Eden R J, Landshoff P V, Olive D I and Poikinghorn J C 1966 The Analytic S-Matrix (Cambridge: Cambridge University Press)
15. Zinn-Justin J 1977 Salamanca 1977 (Lecture Notes in Physics vol 126) ed J A Azcerraga (Berlin: Springer) p 77
16. Zinn-Justin J 1981 Phys. Rep. 70 109
17. Carlitz R N and Nicole D A 1985 Ann. Phys., NY 164 411
18. Carlitz R N 1984 Pittsburgh preprint PITT-19-84
19. Nicole D A and Walters P J 1988 J. Phys. A: Math. Gen. 21 2351
20. Millard P A 1985 Nucl. Phys. B 259 266
21. Garrison J C and Wright E M 1985 Phys. Lett. A 108 129
22. Voros A 1983 Ann. Inst. Henri Poincaré A 39 211
23. Berry M V 1988 Proc. R. Soc. A 422 7
24. Berry M V 1990 Proc. R. Soc. A 427 241
25. Silverstone H 1985 Phys. Rev. Lett. 55 2523-6
26. Berry M V and Howls C J 1990 Proc. R. Soc. A 430 653-67
27. Berry M V and Howls C J 1991 Proc. R. Soc. A 434 657-75
28. Daalhuis Olde A B 1998 Proc. R. Soc. A 445 1-29
29. Delabaere E, Dillinger H and Pham F 1997 J. Math. Phys. 38 6126-84
30. Delabaere E and Pham F Resurgent methods in semiclassical asymptotics Ann. Inst. Henri Poincaré Phys. Theor. at press
31. Ecalle J Cinq application des fonctions resurgentes Publ. Math. D'Orsay (Orsay: Universite Paris-Sud)
32. Ecalle J 1994 Weighted products and parametric resurgence Analyse Algebrique des Perturbations Singulieres I: Methodes Resurgentes Travaux en Course (Paris: Hermann) pp 7-49
33. Sternin B and Shatalov V 1996 Borel-Laplace Transform and Asymptotic Theory (Boca Raton, FL: CRC Press)
34. Fröman N and Fröman P O 1998 J. Math. Phys. 39 4417-29
35. Balian R, Parisi G and Voros A 1979 Feynman Path Integrals (Lecture Notes in Physics vol 106) (Berlin: Springer) p 337
36. Landau L D and Lifshitz E M 1965 Quantum Mechanics. Nonrelativistic Theory (Oxford: Pergamon)
37. Bateman H 1953 Higher Transcendental Functions (New York: McGraw-Hill) p 100 (formula (12))
38. Joye A and Pfister C-H 1993 J. Math. Phys. 34 454-79
39. Hagedorn G A and Joye A 1998 Ann. Inst. Henri Poincare. Phys. Theor. 68 85-134
40. Combes J-M and Hislop P D 1991 Commun. Math. Phys. 140 291-320
41. Bentosela F and Grecchi V 1991 Commun. Math. Phys. 142 169-92
42. Fedoryuk M V 1983 Asymptotic Methods for Linear Ordinary Differential Equations (Moscow: Nauka) (in Russian)