SO-q(N) covariant differential calculus on quantum space and quantum deformation of Schrodinger equation

We construct a differential calculus on theN-dimensional non-commutative Euclidean space, i.e., the space on which the quantum groupSO q (N) is acting. The differential calculus is required to be manifestly covariant underSO q (N) transformations. Using this calculus, we consider the Schrodinger equation corresponding to the harmonic oscillator in the limit ofq→1. The solution of it is given byq-deformed functions.