Lie-algebraic discretization of differential equations

Details Lie-algebraic discretization of differential equations Lie-algebraic discretization of differential equations

1995-01-02

arxiv.org/abs/funct-an/9501001v2

Mod. Phys. Lett. A10 (1995) 1795-1802

Physics

High Energy Physics

High Energy Physics - Lattice

11 pages, LaTeX (a few enlightening remarks added, typos corrected)

Scientific paper

10.1142/S0217732395001927

A certain representation for the Heisenberg algebra in finite-difference operators is established. The Lie-algebraic procedure of discretization of differential equations with isospectral property is proposed. Using $sl_2$-algebra based approach, (quasi)-exactly-solvable finite-difference equations are described. It is shown that the operators having the Hahn, Charlier and Meixner polynomials as the eigenfunctions are reproduced in present approach as some particular cases. A discrete version of the classical orthogonal polynomials (like Hermite, Laguerre, Legendre and Jacobi ones) is introduced.

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