LIE ALGEBRAIC DISCRETIZATION OF DIFFERENTIAL-EQUATIONS

A certain representation for the Heisenberg algebra in finite differen ce operators is established. The Lie algebraic procedure of discretiza tion of differential equations with isospectral property is proposed. Using sl(2)-algebra based approach, (quasi)-exactly-solvable finite di fference equations are described. It is shown that the operators havin g the Hahn, Charlier and Meissner polynomials as the eigenfunctions ar e reproduced in the present approach as some particular cases. A discr ete version of the classical orthogonal polynomials (like Hermite, Lag uerre, Legendre and Jacobi ones) is introduced.