  In the long wavelength limit, Maxwell-Chern-Simmon model and the dynamics of
a particle in a plane under an external magnetic field perpendicular to that
plane are identical. The self adjoint extension of such a problem depends on
the value of angular momentum quantum number $l$. In this article, we have
shown that for $l\neq 0$, the operator describing the Landau level
wave-function is self adjoint; whereas, for $l=0$, infinite number of
self-adjoint extension by an one parameter unitary mapping is possible.
