Quantum-Mechanical Model of an Electron with Self-Consistent Electrostatic Field
Keywords:Dirac equation, Klein–Gordon equation, charge conservation law, electromagnetic field, bispinor, quaternion
A possibility to construct a theory for an electron on the basis of the Dirac equation, where the electromagnetic field potentials are defined as those created by the electron itself, has been analyzed. It is shown that the energy conservation law is obeyed for the combined electromagnetic+bispinor field of an isolated electron. A stationary quasilinear system of equations for the electrostatic+bispinor field is formulated in terms of the quaternion algebra. The quasilinear problem for the electrostatic model of an electron is analyzed. The absence of singularities in the bispinor field components and the density of the electric charge distributed within electron’s central region whose radius is about the Compton length is demonstrated.
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