The bicovariant differential calculus on quantum groups being defined by Woronowicz and later worked out explicitly by Carow-Watamura et at. and Jurčo for the real quantum groups SUq(N) and SOq(N) through a systematic construction of the bicovariant bimodules of these quantum groups is reviewed for SUq(2) and SOq(N). The resulting vector fields build representations of the quantized universal enveloping algebras acting as covariant differential operators on the quantum groups and their associated quantum spaces. As an application a free particle stationary wave equation on quantum space is formulated and solved in terms of a complete set of energy eigenfunctions.
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