We quantize the abelian Chern-Simons theory coupled to non-relativistic
matter field on a torus without invoking the flux quantization. Through a
series of canonical transformations which is equivalent to solving the Gauss
constraint, we obtain an effective hamiltonian density with periodic matter
field. We also obtain the many-anyon Schr\"odinger equation with periodic
Aharonov-Bohm potentials and analyze the periodic property of the wavefunction.
Some comments are given on the different features of our approach from the
previous ones.Comment: 24, SNUTP-93-9