  We study the quantum propagator in the semiclassical limit with sharp
confining potentials. Including the energy-dependent scattering phase due to
sharp confining potential, the modified Van Vleck's formula is derived. We also
discuss the close relations among quantum statistics, discrete gauge symmetry,
and hard-wall constraints. Most of all, we formulate a new quantization rule
that applies to {\it both} smooth and sharp boundary potentials. It provides an
easy way to compute quantized energies in the semiclassical limit and is
extremely useful for many physical systems.
