Hall effect on non-commutative plane with space-space non-commutativity and momentum-momentum non-commutativity

Abstract

In this paper we consider the non-commutative plane with both space-space non-commutativity and momentum-momentum non-commutativity. We study the hamiltonian for an an electron moving on the non-commutative plane in the uniform external electric field along the x-axis and the uniform external magnetic field which is perpendicular to the plane. We solve the Schrödinger equation for this hamiltonian by using the standard factorization method and compute the Hall conductivity.