  It is shown that the non-commutativity in quantum Hall system may get
modified. The self-adjoint extension of the corresponding Hamiltonian leads to
a family of non-commutative geometries labeled by the self-adjoint extension
parameters. We explicitly perform an exact calculation using a singular
interaction and show that, when projected to a certain Landau level, the
emergent non-commutative geometries of the projected coordinates belong to a
one parameter family. There is a possibility of obtaining the filling fraction
of fractional quantum Hall effect by suitably choosing the value of the
self-adjoint extension parameter.
