I’ve uploaded in the preprints webpage of Maths Department, University of Coimbra the manuscript entitled
“Fock spaces, Landau operators and the time-harmonic Maxwell equations.”
done in collaboration with Denis Constales (Ghent University, Belgium) and Rolf Soeren Krausshar (Technical University Darmstad, Germany). Link for the preprint and abstract of the paper follows below.
We are willing to receive your feedback after you read the manuscript.
|[10-47]||Denis Constales, Nelson Faustino e Rolf Soren Krausshar,|
|Fock spaces, Landau operators and the time-harmonic Maxwell equations.|
|pdf | fascículo A5|
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 confining massive spinor fields.
Keywords: Time-harmonic Maxwell equations, Clifford-Hermite expansions, Landau operators.
AMS Subject Classification (2000): 30G35, 33C55, 78A25, 81Q05, 81V10.