Wigner Functions for the Landau Problem in Noncommutative Spaces

Details Wigner Functions for the Landau Problem in Noncommutative Spaces Wigner Functions for the Landau Problem in Noncommutative Spaces

2002-02-10

arxiv.org/abs/hep-th/0202062v1

Mod.Phys.Lett. A17 (2002) 1937-1944

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

10.1142/S0217732302008356

An electron moving on plane in a uniform magnetic field orthogonal to plane is known as the Landau problem. Wigner functions for the Landau problem when the plane is noncommutative are found employing solutions of the Schroedinger equation as well as solving the ordinary *-genvalue equation in terms of an effective Hamiltonian. Then, we let momenta and coordinates of the phase space be noncommutative and introduce a generalized *-genvalue equation. We solve this equation to find the related Wigner functions and show that under an appropriate choice of noncommutativity relations they are independent of noncommutativity parameter.

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