Ehrenfest theorem in relativistic quantum theory
Abstract
Ehrenfest theorem is extended to the relativistic quantum theory of charged particles, moving under the influence of a classical electromagnetic field. In order to extend the original Ehrenfest result to the relativistic domain we bypassed the problems with the relativistic position operator by deriving directly Newton's second law. Our approach is characterized by its universality. The detailed form of the wave equation is not needed. All that is required is the existence of the conserved electric fourcurrent built from the particle wave function. The derivation is based on the conservation laws for the energy and momentum. *The B W Shore Memorial Issue of the Journal of Physics B.
 Publication:

Journal of Physics B Atomic Molecular Physics
 Pub Date:
 June 2022
 DOI:
 10.1088/13616455/ac65c6
 arXiv:
 arXiv:2111.10798
 Bibcode:
 2022JPhB...55k4001B
 Keywords:

 Ehrenfest theorem;
 relativistic wave equations;
 relativistic Newton's law;
 energymomentum tensor;
 Quantum Physics
 EPrint:
 Submitted to: Coherent Control: Photons, Atoms and Molecules The B W Shore Memorial Issue of the Journal of Physics B