  A two dimensional surface can be considered as three dimensional shell whose
thickness is negligible in comparison with the dimension of the whole system.
The quantum mechanics on surface can be first formulated in the bulk and the
limit of vanishing thickness is then taken. The gradient operator and the
Laplace operator originally defined in bulk converges to the geometric ones on
the surface, and the so-called geometric momentum and geometric potential are
obtained. On the surface of two dimensional sphere the geometric momentum in
the Monge parametrization is explicitly explored. Dirac's theory on
second-class constrained motion is resorted to for accounting for the
commutator [x_{i},p_{j}]=i \hbar({\delta}_{ij}-x_{i}x_{j}/r^2) rather than
[x_{i},p_{j}]=i\hbar{\delta}_{ij} that does not hold true any more. This
geometric momentum is geometric invariant under parameters transformation, and
self-adjoint.
