We construct a differential calculus on the N-dimensional non-commutative Euclidean space, i.e., the space on which the quantum group SOq(N) is acting. The differential calculus is required to be manifestly covariant under SOq(N) transformations. Using this calculus, we consider the Schrödinger equation corresponding to the harmonic oscillator in the limit of q→1. The solution of it is given by q-deformed functions.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)