Integrable systems on the lattice and orthogonal polynomials of discrete variable

Journal of Computational and Applied Mathematics

Volumn 153, Issue 1-2, 2003, Pages 321-330

  Lorente, Miguel ^a  

^a UNIVERSITY OF OVIEDO   (Spain)

Author keywords

Difference equations; Discrete models; Integrable systems; Orthogonal polynomials; Raising and lowering operators

Indexed keywords

POLYNOMIALS; PROBLEM SOLVING; QUANTUM THEORY;

DISCRETE VARIABLES;

COMPUTATIONAL METHODS;

MATHEMATICAL ANALYSIS;

EID: 0037381212     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(02)00592-7     Document Type: Article

References (10)

1. J.C. Baez, An introduction to spin foam model of background free theory and quantum gravity, In: H. Gausteter et al., (Ed.), Geometry and Quantum Physics, Lecture Notes in Physics, Vol. 543, Springer, Berlin, 2000.
2. T.H. Koornwinder, Meixner-Pollaczek polynomials and the Heisenberg algebra, J. Math. Phys. 30 (1989) 767-769.
3. D. Levy, L. Vinet, P. Winternitz (Eds.), Symmetries and Integrability of Difference Equations, American Mathematical Society, Providence, RI, 1996.
4. M. Lorente, On some integrable one-dimensional quantum systems, Phys. Lett. B 232 (1989) 345-350.
5. M. Lorente, A new scheme for the Klein-Gordon and Dirac fields on the lattice with axial anomaly, J. Group Theory Phys. 1 (1993) 105-121.
6. M. Lorente, Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom, Phys. Lett. A 285 (2001) 119-126.
7. M. Lorente, Raising and lowering operators, factorization and differential /difference operators of hypergeometric type, J. Phys. A 34 (2001) 569-588.
8. I. Montvay, G. Münster, Quantum Field Theories on a Lattice, Cambridge University Press, Cambridge, 1994.
9. A.F.Nikiforov, S.K. Suslov, V.B. Uvarov, Classical Orthogonal polynomials of Discrete Variable, Springer, Berlin, 1991
10. A.M. Perelomov, Quantum integrable systems and Clebsch-Gordon series, J. Phys. A 31 (1998) L31-L37.