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arXiv · funct-an/9501001

Lie-algebraic discretization of differential equations

Yuri Smirnov·Alexander Turbiner
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Abstract

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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BibTeXRIS

Yuri Smirnov, Alexander Turbiner. 1995-06-16. Lie-algebraic discretization of differential equations. https://doi.org/10.1142/s0217732395001927

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