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College Physics

Landau quantization of neutral atom in an electromagnetic field in noncommutative quantum mechanics

Obulkasim Asiyagul

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

Within the scope of noncommutative quantum mechanics,we study the Landau problem for neutral atoms in the presence of an external electromagnetic field.By solving the time independent Schrdinger equations in both noncommutative space and noncommutative phase space,we obtain explicit experession of Landau energy levels and corresponding eigenfunctions,at the asme time,we claculate the energy correction terms caused by noncommutativity,respectively.

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Within the scope of noncommutative quantum mechanics,we study the Landau problem for neutral atoms in the presence of an external electromagnetic field.By solving the time independent Schrdinger equations in both noncommutative space and noncommutative phase space,we obtain explicit experession of Landau energy levels and corresponding eigenfunctions,at the asme time,we claculate the energy correction terms caused by noncommutativity,respectively.
We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric qaudrupole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field, we give the Schrödinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrödinger equations both on a noncommutative space and a noncommutative phase space, we obtain quantum phases of the electric quadrupole moment, respectively. We demonstrate that these phases are geometric and dispersive.
An electron moving on plane in a uniform magnetic field orthogonal to the plane is known as the Landau problem. Wigner functions for the Landau problem when the plane is noncommutative are found employing solutions of the Schrödinger 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.
The Aharonov-Bohm (AB) effect in non-commutative quantum mechanics (NCQM) is studied. First, by introducing a shift for the magnetic vector potential we give the Schrddoto\\ddot{o}ddotodinger equations in the presence of a magnetic field on NC space and NC phase space, respectively. Then by solving the Schrddoto\\ddot{o}ddotodinger equations, we obtain the Aharonov-Bohm (AB) phase on NC space and NC phase space, respectively.