Noncommutative Quantum Mechanics: The Two-Dimensional Central Field

Details Noncommutative Quantum Mechanics: The Two-Dimensional Central Field Noncommutative Quantum Mechanics: The Two-Dimensional Central Field

2001-06-14

arxiv.org/abs/hep-th/0106125v2

Int.J.Mod.Phys. A17 (2002) 2555-2566

Physics

High Energy Physics

High Energy Physics - Theory

new references added

Scientific paper

10.1142/S0217751X02010960

Quantum mechanics in a noncommutative plane is considered. For a general two dimensional central field, we find that the theory can be perturbatively solved for large values of the noncommutative parameter ($\theta$) and explicit expressions for the eigenstates and eigenvalues are given. The Green function is explicitly obtained and we show that it can be expressed as an infinite series. For polynomial type potentials, we found a smooth limit for small values of $\theta$ and for non-polynomial ones this limit is necessarily abrupt. The Landau problem, as a limit case of a noncommutative system, is also considered.

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