Lie-algebraic discretization of differential equations

  title={Lie-algebraic discretization of differential equations},
  author={Yu. F. Smirnov and Alexander V. Turbiner},
  journal={Modern Physics Letters A},
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 sl2-algebra based approach, (quasi)-exactly-solvable finite difference equations are described. It is shown that the operators having the Hahn, Charlier and Meissner polynomials as the eigenfunctions are reproduced in the present approach as some particular cases. A discrete version… Expand
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Turbiner “ Quasiexactlysolvable problems and sl ( 2 , R ) algebra ”
  • Comm . Math . Phys . Journ . Phys . A