Wronskian and Casorati determinant representations for Darboux-Pöschl- Teller potentials and their difference extensions

Journal of Physics A: Mathematical and Theoretical

Volumn 42, Issue 40, 2009, Pages

  Gaillard, P ^a   Matveev, V B ^a,b  

^a UNIVERSITÉ DE BOURGOGNE   (France)

^b MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70449688255     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/42/40/404009     Document Type: Article

References (30)

1. Berest Y 1997 Solution of a restricted Hadamard problem on Minkowski space Comm. Pure Appl. Math. 50 1019-52
2. Berest Y and Loutsenko I 1997 Huygens principle in Minkowski space and soliton solutions to the Korteweg de Vries equation Commun. Math. Phys. 190 113-32
3. Berest Y 2008 Heat kernel coefficients for two-dimensional Schrödinger equation Commun. Math. Phys. 283 853-60
4. Crum M 1955 Associated Sturm-Liouville system Q. J. Math. 6 121-8
5. Darboux G 1882 Sur une équation linéaire C. R. Acad. Sci. I 1645-8
6. Darboux G 1882 Sur une proposition relative aux équations linéaires C. R. Acad. Sci., Paris I 1456
7. Darboux G 1915 Leçons sur la théorie des Surfaces vol 2 2nd edn (Paris: Gauthier-Villars) pp 210-5
8. van Diejen J F and Kirillov A N 2000 A combinatorial formula for the associated Legendre functions of integer degree Adv. Math. 149 61-8
9. van Diejen J F and Kirillov A N 2001 Determinantal formulas for zonal spherical functions on hyperboloids Math. Ann. 319 215-34
10. van Diejen J F and Kirillov A N 2000 Formulas for q-spherical functions using inverse scattering theory of reflectionless Jacobi operators Commun. Math. Phys. 210 335-69
11. van Diejen J F 1994 Integrability of difference Calogero-Moser systems J. Math. Phys. 35 2983-3004
12. Gaillard P and Matveev V B 2002 Wronskian Addition Formula and its Applications vol MPI 02-31 (Bonn: Max-Planck-Institut für Mathematik) pp 1-17
13. Gaillard P 2004 A new family of deformations of Darboux-Pöschl- Teller potentials Lett. Math. Phys. 68 77-90
14. Gaillard P and Matveev V B 2009 New formulas for the eigenfunctions of the two-particle difference Calogero-Moser system Lett. Math. Phys. 89 (July) at press (published online) (DOI 10.1007/s1105-009-0315-6)
15. Gaillard P and Matveev V B Deformed Darboux-Pöschl-Teller equation and Askey-Wilson functions in preparation
16. Ismail M E and Rahman M 1991 The associated Askey-Wilson polynomials Trans. Am. Math. Soc. 328 201-37
17. Matveev V B 1979 Darboux transformations and the solutions of KP equation depending on the functional parameters Lett. Math. Phys. 3 213-6
18. Matveev V B and Salle M A 1991 Darboux Transformations and Solitons (Series in Nonlinear Dynamics) (Berlin: Springer)
19. Matveev V B 2000 Darboux transformations, covariance theorems and integrable systems L D Faddeev's Seminar on Mathematical Physics 201 ed M A Semenov-Tyan-Shanskij Am. Math. Soc. Transl. 179-209
20. Matveev V B 1979 Darboux transformation and explicit solutions of differential-difference and difference-difference evolution equations: I Lett. Math. Phys. 3 217-22
21. Matveev V B and Salle M A 1979 Differential-difference evolution equations: II. Darboux transformations for the Toda lattice Lett. Math. Phys. 3 425-30
22. Matveev V B 2006 Functional difference deformations of Darboux-Pöschl-Teller potentials Proc. NATO ARW Workshop (Elba, Italy, September 2002) (Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete) vols 1 and 2 ed L D Faddeev and P Van Moerbeke (Berlin: Springer) pp 191-208
23. Matveev V B 2002 Functional difference analogue analogues of Darboux-Pöschl-Teller potentials (Preprint Series No 125) (Bonn: Max-Planck-Institut für Mathematik)
24. Odake S and Sasaki R 2009 Crum's theorem for discrete quantum mechanics arXiv:0902.2593 [math-ph]
25. Pöschl G and Teller E 1933 Bemerkungen zur Quantenmechanik des anharmonischen oszillators Z. Phys. 83 143-51
26. Proskuryakov I V 1984 Recollection of Problems in Linear Algebra (Moscow: Nauka) p 37 (in Russian)
27. Ruisjenaars S N M 1999 Generalized Lamé functions: II. Hyperbolic and trigonometric specialisations J. Math. Phys. 40 1627-63
28. Spiridonov V and Zhedanov A 1995 Discrete Darboux transformations, the discrete time Toda lattice and the Askey-Wilson polynomials Ann. Phys. 2 370-98
29. Spiridonov V and Zhedanov A 1995 Discrete reflectionless potentials, quantum algebras, and q-orthogonal polynomials Ann. Phys. 237 126-46
30. Vladut S 2001 Isogeny class and Frobenius root statistics for Abelian varieties over finite fields Mosc. Math. J. 1 125-40