Structure of avoided crossings for eigenvalues related to equations of Heun's class

Journal of Physics A: Mathematical and General

Volumn 30, Issue 2, 1997, Pages 673-687

  Slavyanov, S Yu ^a,c   Veshev, N A ^b  

^a ISAAC NEWTON INSTITUTE FOR MATHEMATICAL SCIENCES   (United Kingdom)

^b SAINT PETERSBURG STATE UNIVERSITY OF AEROSPACE INSTRUMENTATION   (Russian Federation)

^c ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031581623     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/30/2/027     Document Type: Article

References (21)

1. Komarov I V and Slavyanov S Y 1968 The two Coulomb centers problems at large center separation J. Phys. B: At. Mol. Phys. 2
2. 2 J. Exp. Theor. Phys. 1
3. Komarov I V, Ponomarev L I and Slavyanov S Y 1996 Spheroidal and Coulomb Spheroidal Functions (Moscow: Nauka)
4. Komarov I V and Solov'ev E A 1979 Avoided crossings of potential curves in the problem of two Coulomb centers with two strongly different charges Sov. Phys. Theor. Math. Phys. 40 130
5. Ronveaux A 1995 Heun's Differential Equations (Oxford: Oxford University Press)
6. Slavyanov S Y 1969 The asymptotics of Sturm-Liouville singular problems in a large parameter in case of 'close' turning points Differentsialnyje Uravnenija 5
7. Slavyanov S Y 1990 Asymptotic Solutions for One-dimensional Schrödinger Equation (Leningrad: Leningrad University Press) (Engl. transl. 1996 (New York: AMS))
8. Silverstone H J 1985 JWKB connection formula problem revisited via Borel summation Phys. Rev. Lett. 55 2523
9. Delabaere E and Pham F 1996 Resurgent methods in semi-classical asymptotics, in press
10. Khuat-duy K and Lebeof P 1993 Multiresonance tunneling effects in double-well potential Appl. Phys. Lett. 63
11. Solov'ev E A 1989 Nonadiabatic transitions in atomic collisions Sov. Phys.-Usp. 32 228
12. Berry M V 1984 The adiabatic limit and the semiclassical limit J. Phys. A: Math. Gen. 17 1225-33
13. Slavyanov S Yu, Lay W and Seeger A 1995 Classification Heun's Differential Equations (Oxford: Oxford University Press)
14. Lay W, Seeger A and Slavyanov S Yu 1995 A generalization of the Riemann scheme for equations of the hypergeometric class Preprint Universität Stuttgart 9615
15. Seeger A, Lay W and Slavyanov S Yu 1995 Confluence of Fuchsian second-order differential equations Theor. Math. Fys. 104
16. Wentzel G 1926 Eine Verallgemeinerung der Quantenbedingung für die Zwecke der Wellenmechanik Z. Phys. 33
17. Cohen J and Slavyanov S Yu 1992 Semiclassical asymptotics of the spectrum for the lower states of an anharmonic oscillator St Petersburg Math. J. 3 355-61
18. my(z) =0. Dokl. Acad. Sci. USSR 285
19. Costin O and Kruskal M 1996 Optimal asymptotic estimates and rigorous asymptotics beyond all orders for a class of ordinary differential equations Proc. R. Soc. in press
20. Berry M V 1989 Uniform asymptotic smoothing of Stokes' discontinuities Proc. R. Soc. A 422 7-21
21. McLeod J B 1992 Smoothing of Stokes' discontinuities Proc. R. Soc. 437 343-54