Application of supersymmetry to a coupled system of equations: the concept of a superpotential matrix

We apply supersymmetric quantum mechanics (SUSY QM) to multidimensional Schroedinger equations involving nonseparable potentials, which result in a system of coupled differential equations, where instead of the conventional definition of a scalar superpotential we introduce a superpotential matrix and succeed in applying SUSY QM to the coupled system. Finally, we discuss the shape-invariance condition for the potential matrix of such a system. (author)