  A generalization of the Dirac's canonical quantization theory for a system
with second-class constraints is proposed as the fundamental commutation
relations that are constituted by all commutators between positions, momenta
and Hamiltonian so they are simultaneously quantized in a self-consistent
manner, rather than by those between merely positions and momenta so the theory
either contains redundant freedoms or conflicts with experiments. The
application of the generalized theory to quantum motion on a torus leads to two
remarkable results: i) The theory formulated purely on the torus, i.e., based
on the so-called the purely intrinsic geometry, conflicts with itself. So it
provides an explanation why an intrinsic examination of quantum motion on torus
within the Schrodinger formalism is improper. ii) An extrinsic examination of
the torus as a submanifold in three dimensional flat space turns out to be
self-consistent and the resultant momenta and Hamiltonian are satisfactory all
around.
