  In previous works we have studied spin-3/2 fields near 4-dimensional
Schwarzschild black holes. The techniques we developed in that case have now
been extended here to show that it is possible to determine the potential of
spin-3/2 fields near $D$-dimensional black holes by exploiting the radial
symmetry of the system. This removes the need to use the Newman-Penrose
formalism, which is difficult to extend to $D$-dimensional space-times. In this
paper we will derive a general $D$-dimensional gauge invariant effective
potential for spin-3/2 fields near black hole systems. We then use this
potential to determine the quasi-normal modes and absorption probabilities of
spin-3/2 fields near a $D$-dimensional Schwarzschild black hole.
