Symmetries of linear difference equations via umbral calculus
Abstract:
We propose a general approach to the study of Lie symmetries of difference
equations. This approach is based on the axiomatic theory of finite difference
operators (introduced by G.C. Rota). In particular, our formalism is applied
to the Schroedinger equation in order to obtain a realization of quantum
mechanics on a lattice which preserves the properties of integrability,
superintegrability and exact solvability.
This is joint work with Decio Levi and Pavel Winternitz