Non-relativistic Schroedinger theory on q-deformed quantum spaces I, Mathematical framework and equations of motion

Abstract

The aim of these three papers (I, II, and III) is to develop a q-deformed version of non-relativistic Schroedinger theory. Paper I introduces the fundamental mathematical and physical concepts. The braided line and the three-dimensional q-deformed Euclidean space play the role of position space. For both cases the algebraic framework is extended by a time element. A short review of the elements of q-deformed analysis on the spaces under consideration is given. The time evolution operator is introduced in a consistent way and its basic properties are discussed. These reasonings are continued by proposing q-deformed analogs of the Schroedinger and the Heisenberg picture.

arXiv comment48 pages, no figures, Latex

References in corpus (6)

• Algebraic {$q$}-Integration and Fourier Theory on Quantum and Braided Spaces
• Differential Calculus on Iso_q (N), Quantum Poincare' Algebra and q - Gravity
• Introduction to Braided Geometry and $q$-Minkowski Space
• q-Integration on Quantum Spaces
• q-Translations on quantum spaces
• Braided products for quantum spaces