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Chinese Physics

Coherent Landau states with gauge invariance

Tian Xu, Zhao Zhong-Yun, Li Ming-Fa

Published Sep 28, 2004• 11 citations
Publisher

Abstract

Coherent states for the Landau system (planar charged particle moving in a uniform magnetic field) are developed. It is convenient to use these states to describe the circular motion of the charged particle. The results obtained do not depend on gauges.
DOI
10.1088/1009-1963/13/10/012

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We study the problem of a charged particle in a uniform magnetic field with two different gauges, known as Landau and symmetric gauges. By using a similarity transformation in terms of the displacement operator we show that, for the Landau gauge, the eigenfunctions for this problem are the harmonic oscillator number coherent states. In the symmetric gauge, we calculate the SU(1,1)SU(1,1)SU(1,1) Perelomov number coherent states for this problem in cylindrical coordinates in a closed form. Finally, we show that these Perelomov number coherent states are related to the harmonic oscillator number coherent states by the contraction of the SU(1,1)SU(1,1)SU(1,1) group to the Heisenberg-Weyl group.