Abstract
Based on a suitable linear combination of the physical and un-physical electromagnetic potentials, the radiation reaction potentials have been calculated. Through the near zone expansion of the potentials, it has been shown that in either of the relativistic and non-relativistic cases the outgoing (radiated) energy of the electrons orbiting the nucleus is substituted by incoming (electromagnetic radiation reaction) energy. This means that energy is conserved and the classical hydrogen-like atoms are stable.
Highlights
The interaction of a particle with it’s own field produces the phenomenon of radiation reaction
Through the near zone expansion of the potentials, it has been shown that in either of the relativistic and non-relativistic cases the outgoing energy of the electrons orbiting the nucleus is substituted by incoming energy
This means that energy is conserved and the classical hydrogen-like atoms are stable
Summary
The interaction of a particle with it’s own field produces the phenomenon of radiation reaction. While the potential of Equation (1.2) does not exert a force on the charged particle, it is just as singular as the retarded potential in the vicinity of the world line. This follows from the fact that Ar et , Aa dv and AS all satisfy Equation (1.1), whose source term is infinite on the world line. Because AS is just as singular as Ar et , removing it from the retarded solution gives rise to a potential that is well behaved in a neighborhood of the world line and because AS not to affect the motion of the charged particle, this new potential must be entirely responsible for the radiation reaction. The results show that in either of the relativistic and non-relativistic cases, the energy is conserved and the classical hydrogen-like atoms are stable
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