Integral equation for a particle in an electric field

N. Boudiaf, Abdeldjalil Merdaci, L. Chétouani

The Green's function for a Dirac particle submitted to a constant electric field is analytically calculated by using a path integral supersymmetric approach via an auxiliary equation which was introduced. The wavefunctions have been exactly obtained.

Vladimir I. Man’ko, Evgeny V Shchukin

Vladimir I. Man’ko, Evgeny V Shchukin

Green function and linear integrals of motion for a charged particle moving in electric field are discussed. Wigner function and tomogram of the ststionary states of the charge are obtained. Connection of quantum propagators for Schrodinger evolution equation, Moyal evolution equation and evolution equation in tomographic probability representation for charge moving in electric field is discussed.

Takashi Ichinose, Hiroshi Tamura

Countably additive path space measures are constructed, in two space-time dimensions, to give rigorous path integral formulas representing the fundamental solution of the Cauchy problem for the Dirac equation as well as the retarded and advanced propagator for the Dirac particle. The theory also applies to a free particle, a particle in a central electric field and a particle in parallel electric and uniform magnetic fields in four-dimensional space-time.