Geometric quantization of a particle in a perpendicular magnetic field
The authors of this paper study the quantization of a particle in the plane under the influence of a perpendicular magnetic field, using geometric quantization and half-forms in the Hilbert space of holomorphic functions. Relying on a judiciously chosen coordinate transformation they are able to convert the problem into a system of harmonic oscillators. The later problem is solved directly and, as a bonus, the relationship between different representations is highlighted as well. Finally, the authors point out the isomorphism between the holomorphic representation and the standard Schrödinger representation.
scientific article; zbMATH DE number 6683085