  Quantum mechanics in conical space is studied by the path integral method. It
is shown that the curvature effect gives rise to an effective potential in the
radial path integral. It is further shown that the radial path integral in
conical space can be reduced to a form identical with that in flat space when
the discrete angular momentum of each partial wave is replaced by a specific
non-integral angular momentum. The effective potential is found proportional to
the squared mean curvature of the conical surface embedded in Euclidean space.
The path integral calculation is compatible with the Schr\"odinger equation
modified with the Gaussian and the mean curvature.
