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2016 Geometric Quantization of a Particle in a Perpendicular Magnetic Field
Guillermo Capobianco, Walter Reartes
J. Geom. Symmetry Phys. 41: 17-32 (2016). DOI: 10.7546/jgsp-41-2016-17-32

Abstract

In this paper we develop the quantization of a particle in the plane under the influence of a perpendicular magnetic field using the geometric quantization with half--forms in Hilbert space of holomorphic functions. An original coordinate transformation is applied to convert the problem into a system of harmonic oscillators. Then, it is solved highlighting the relationship between different representations. We emphasize the isomorphism between the holomorphic representation and the Schrödinger representation.

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Guillermo Capobianco. Walter Reartes. "Geometric Quantization of a Particle in a Perpendicular Magnetic Field." J. Geom. Symmetry Phys. 41 17 - 32, 2016. https://doi.org/10.7546/jgsp-41-2016-17-32

Information

Published: 2016
First available in Project Euclid: 31 May 2017

zbMATH: 1373.53123
MathSciNet: MR3585164
Digital Object Identifier: 10.7546/jgsp-41-2016-17-32

Rights: Copyright © 2016 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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