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arXiv · 0906.0388

Semiclassical and quantum description of motion on noncommutative plane

M. C. Baldiotti·J. P. Gazeau·D. M. Gitman
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Abstract

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 θ-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 θ-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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M. C. Baldiotti, J. P. Gazeau, D. M. Gitman. 2009-06-03. Semiclassical and quantum description of motion on noncommutative plane. https://doi.org/10.1016/j.physleta.2009.08.059

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