  We study an $N + 1$ dimensional generalization of the Schwarzschild black
hole from the quantum mechanical viewpoint. It is shown that the mass loss rate
of this higher dimensional black hole due to the black hole radiation is
proportional to $1 \over r^{N-1}$ where $r$ is the radial coordinate. This fact
implies that except in four dimensions the quantum formalism developed in this
letter gives a different result with respect to the mass loss rate from the
semiclassical formalism where the Stefan-Bolzmann formula for a blackbody
radiation is used. As shown previously in the study of the four dimensional
Schwarzschild metric, the wave function in this case has also quite curious
features that it is singular owing to strong quantum fluctuation of the
gravitational field at the singularity while completely regular in the other
regions of the spacetime.
