# Interaction Theory of Balanced Charges

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## Abstract

In this chapter we consider interaction of many charges. In point-like regimes, where the charges are weell-separated in space, we derive Newton’s law of motion. The derivation is in the spirit of the Ehrenfest theorem. In the relativistic case, we obtain the relativistic version of Newton’s law where the mass of a charge is determined by its energy according to Einstein’s formula, and the rest mass is an integral of motion. When charges are in a close proximity as in Hydrogen atom, they are described by multiharmonic solutions. An analysis of corresponding system shows that it has discrete energy levels as in Schrödinger model.

## Copyright information

© Springer-Verlag London 2016