Physics – Mathematical Physics
Scientific paper
2009-10-19
Physics
Mathematical Physics
Typos are corrected, some editing made
Scientific paper
We study here a number of mathematical problems related to our recently introduced neoclassical theory for the electromagnetic phenomena in which charges are represented by complex valued wave functions as in the Schrodinger wave mechanics. Dynamics of charges in the non-relativistic case is governed by a system of nonlinear Schrodinger equations coupled with the electromagnetic fields, and we prove for it that the centers of wave functions converge in macroscopic regimes to trajectories of points governed by the Newton's equations with the Lorentz forces provided the wave functions remain localized. Exact solutions in the form of localized accelerating solitons are found. Our studies of a class of time multiharmonic solutions of the same field equations show that they satisfy Planck-Einstein relation and that the energy levels of the nonlinear eigenvalue problem for the hydrogen atom converge to the well-known energy levels of the linear Schrodinger operator when the free charge size is much larger than the Bohr radius.
Babin Anatoli
Figotin Alexander
No associations
LandOfFree
Some mathematical problems in a neoclassical theory of electric charges does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Some mathematical problems in a neoclassical theory of electric charges, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some mathematical problems in a neoclassical theory of electric charges will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-716539