Physics – Mathematical Physics
Scientific paper
2010-11-21
J. Phys. A: Math. Theor. 44 135303 (2011)
Physics
Mathematical Physics
Exposition improved; Some typos corrected; Accepted for publication in J.Phys.A (February 2011). http://www.mat.uc.pt/preprint
Scientific paper
10.1088/1751-8113/44/13/135303
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 Schr\"odinger equations with natural applications in relativistic quantum mechanics concerning massive spinor fields.
Constales Denis
Faustino Nelson
Krausshar Soeren
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