On quantum algebra symmetries of discrete Schrödinger equations

Details On quantum algebra symmetries of discrete Schrödinger equations On quantum algebra symmetries of discrete Schrödinger equations

1998-08-10

arxiv.org/abs/math/9808043v1

Mathematics

Quantum Algebra

11 pages, LaTeX

Scientific paper

Two non-standard quantum deformations of the (1+1) Schr\"odinger algebra are identified with the symmetry algebras of either a space or time uniform lattice discretization of the Schr\"odinger equation. For both cases, the deformation parameter of the corresponding Hopf algebra can be interpreted as the step of the lattice. In this context, the introduction of nonlinear maps defining Schr\"odinger and $sl(2,\R)$ quantum algebras with classical commutation rules turns out to be relevant. The problem of finding a quantum algebra linked to the full space-time discretization is also discussed.

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