  A fundamental problem regarding the Dirac quantization of a free particle on
an $N-1$ curved hypersurface embedded in $N$($\geq 2$) flat space is the
impossibility to give the same form of the curvature-induced quantum potential,
the geometric potential as commonly called, as that given by the
Schr\"{o}dinger equation method where the particle moves in a region confined
by a thin-layer sandwiching the surface. We resolve this problem by means of
previously proposed scheme that hypothesizes a simultaneous quantization of
positions, momenta, and Hamiltonian, among which the operator-ordering-free
section is identified and is then found sufficient to lead to the expected form
of geometric potential.
