The multidimensional Darboux transformation

Journal of Geometry and Physics

Volumn 26, Issue 3-4, 1998, Pages 202-226

  González López, Artemio ^a   Kamran, Niky ^b,c  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b FIELDS INSTITUTE   (Canada)

^c MCGILL UNIVERSITY   (Canada)

Author keywords

Darboux transformation; Moutard transformation; Quasi exact solvability; Supersymmetric quantum mechanics

Indexed keywords

EID: 0032118567     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(97)00044-2     Document Type: Article

References (16)

1. [1] A.A. Andrianov, N.V. Borissov, M.I. Eides and M.V. Ioffe, Supersymmetric origin of equivalent quantum systems, Phys. Lett. A 109 (1985) 143-148.
2. [2] A.A Andrianov, N.V. Borissov and M.V. Ioffe, The factorization method and quantum systems with equivalent energy spectra, Phys. Lett. A 105 (1984) 19-22.
3. [3] M.M. Crum, Associated Sturm-Liouville equations, Q. J. Math. 6 (1955) 121-127.
4. [4] G. Darboux, Théorie Générale des Surfaces, Vol. II (Gauthier-Villars, Paris, 1888).
5. [5] P. Deift and E. Trubowitz, Inverse scattering on the line, Comm. Pure Appl. Math. 32 (1979) 121-251.
6. [6] A. González-López, N. Kamran and P.J. Olver. New quasi-exactly solvable Hamiltonians in two dimensions, Comm. Math. Phys. 159 (1994) 503-537.
7. [7] A. González-López, N. Kamran and P.J. Olver. Quasi-exact solvability, Contemp. Math. 160 (1994) 113-140.
8. [8] A. González-López, N. Kamran and P.J. Olver, Real Lie algebras of differential operators and quasi-exactly solvable potentials, Phil. Trans. Roy. Soc. London A 354 (1996) 1165-1193.
9. [9] E. Goursat, Leçons Sur l' Intégration des Equations aux Dérivées Partielles du Second Ordre (Hermann, Paris, 1896).
10. [10] L. Infeld and T. Hull, The factorization method, Rev. Modern Phys. 23 (1951) 21-68.
11. [11] N. Kamran and K. Tenenblat. Laplace transformation in higher dimensions, Duke Math. J. 84 (1996) 237-266.
12. xy = λ(x, y), qui admettent une intégrale générale explicite. J. de L'Ecole Polytech, Cahier 45 (1878) 834.
13. [13] A. Ushveridze, Quasi-exactly Solvable Models in Quantum Mechanics (IOP, Bristol, 1994).
14. [14] P.J. Vassiliou, On some geometry associated with a generalised Toda lattice, Bull. Austral. Math. Soc. 49 (1994) 439-462.
15. [15] E. Witten, Dynamical breaking of supersymmetry, Nuclear Phys. B 188 (1981) 513-555.
16. [16] E. Witten, Supersymmetry and Morse theory, J. Differential Geom. 17 (1982) 661-692.