Symmetries of the discrete Schrödinger equation and its quantum deformations

1. Nieto, Luis
2. Negro, Javier
3. Herranz, Francisco
4. Ballesteros, Angel

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DOI: 10.1090/CRMP/025/31 GOOGLE SCHOLAR lock_openAccès ouvert editor

Résumé

After a short revision of the symmetries in the free Schröndiger equation, the nonstandard quantum deformations of the (1+1)- Schrödinger algebra are considered. Two of them are identified with the symmetry algebras of either a space or time uniform lattice discretization of the free Schröndiger equation. For both cases, the deformation parameter of the corresponding Hopf algebra can be interpreted as the step of the lattice. The problem of finding a quantum algebras linked to the full space-time discretization is also discussed.