  As is well known, an external magnetic field in configuration space coupled
to a quantum dynamics induces noncommutativity in its velocity momentum space.
By phase space duality, an external vector potential in the conjugate momentum
sector of the system induces noncommutativity in its configuration space. Such
a rationale for noncommutativity is explored herein for an arbitrary
configuration space of Euclidean geometry. Ordinary quantum mechanics with a
commutative configuration space is revisited first. Through the introduction of
an arbitrary positive definite $*$-product, a one-to-one correspondence between
the Hilbert space of abstract quantum states and that of the enveloping algebra
of the position quantum operators is identified. A parallel discussion is then
presented when configuration space is noncommutative, and thoroughly analysed
when the conjugate magnetic field is momentum independent and nondegenerate.
Once again the space of quantum states may be identified with the enveloping
algebra of the noncommutative position quantum operators. Furthermore when the
positive definite $*$-product is chosen in accordance with the value of the
conjugate magnetic field which determines the commutator algebra of the
coordinate operators, these operators span a Fock algebra of which the
canonical coherent states are the localised noncommutative quantum analogues of
the sharp and structureless local points of the associated commutative
configuration space geometry. These results generalise and justify a posteriori
within the context of ordinary canonical quantisation the heuristic approach to
quantum mechanics in the noncommutative Euclidean plane as constructed and
developed by F. G. Scholtz and his collaborators.
