Abstract

OJEDA-GUILLEN, D.; SALAZAR-RAMIREZ, M.; MOTA, R.D.  and  GRANADOS, V.D.. An algebraic approach to a charged particle in a uniform magnetic field. Rev. mex. fís. E [online]. 2018, vol.64, n.2, pp.127-132. ISSN 1870-3542.

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) 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) group to the Heisenberg-Weyl group.

Keywords : Coherent states; group theory; Landau levels.

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