标题： 李代数离散化微分方程 显示英文标题

标题： Lie-algebraic discretization of differential equations

摘要： 建立了Heisenberg代数在有限差分算符上的一种特定表示。 提出了具有等谱性质的微分方程离散化的李代数方法。 利用基于$sl_2$-代数的方法，描述了（准）完全可解的有限差分方程。 证明了具有Hahn、Charlier和Meixner多项式作为特征函数的算符在当前方法中被重新表述为一些特例。 引入了经典正交多项式（如Hermite、Laguerre、Legendre和Jacobi多项式）的离散版本。 显示英文摘要

摘要： 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.