  The Hermitian Cartesian quantum momentum operator $\mathbf{p}$ for an
embedded surface $M$ in $R^{3}$ is proved to be a constant factor $-i\hbar $
times the mean curvature vector field $H\mathbf{n}$ added to the usual
differential term. With use of this form of momentum operators, the
operator-ordering ambiguity exists in the construction of the correct kinetic
energy operator and three different operator-orderings lead to the same result.
  PACS: 03.65.-w Quantum mechanics, 04.60.Ds Canonical quantization
