Quantum Dynamics on the three-dimensional q-deformed Euclidean Space

I extend the three-dimensional q-deformed Euclidean space by a time element and discuss the algebraic structure of this quantum space together with its differential calculi. Using the star-product formalism, I will give basic operations of q-deformed analysis for the q-deformed Euclidean space with a time element. I show that the time-evolution operator of a quantum system living in the q-deformed Euclidean space is of the same form as in the undeformed case. The reasonings also show that the well-known methods of quantum dynamics apply to quantum systems living in the q-deformed Euclidean space.