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arXiv · 1011.4628

Fock Spaces, Landau Operators and the Regular Solutions of time-harmonic Maxwell equations

Denis Constales·Nelson Faustino·Soeren Krausshar
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Abstract

We investigate the representations of the solutions to Maxwell's equations based on the combination of hypercomplex function-theoretical methods with quantum mechanical methods. Our approach provides us with a characterization for the solutions to the time-harmonic Maxwell system in terms of series expansions involving spherical harmonics resp. spherical monogenics. Also, a thorough investigation for the series representation of the solutions in terms of eigenfunctions of Landau operators that encode $n-$dimensional spinless electrons is given. This new insight should lead to important investigations in the study of regularity and hypo-ellipticity of the solutions to Schrödinger equations with natural applications in relativistic quantum mechanics concerning massive spinor fields.

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Denis Constales, Nelson Faustino, Soeren Krausshar. 2011-02-16. Fock Spaces, Landau Operators and the Regular Solutions of time-harmonic Maxwell equations. https://doi.org/10.1088/1751-8113/44/13/135303

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