Semiclassical and quantum description of motion on noncommutative plane

Details Semiclassical and quantum description of motion on noncommutative plane Semiclassical and quantum description of motion on noncommutative plane

2009-06-01

arxiv.org/abs/0906.0388v2

Phys.Lett.A373:3937-3943,2009

Physics

Quantum Physics

20 pages

Scientific paper

10.1016/j.physleta.2009.08.059

We study the canonical and the coherent state quantization of a particle moving in a magnetic field on a non-commutative plane. Starting from the so called \theta-modified action, we perform the canonical quantization and analyze the gauge dependence of the obtained quantum theory. We construct the Malkin-Man'ko coherent states of the system in question, and the corresponding quantization. On this base, we study the relation between the coherent states and the "classical" trajectories predicted by the \theta-modified action. In addition, we construct different semiclassical states, making use of special properties of circular squeezed states. With the help of these states, we perform the Berezin-Klauder-Toeplitz quantization and present a numerical exploration of the semiclassical behavior of physical quantities in these states.

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