Accession Number : AD0805744

Title :   TECHNICAL REPORT NUMBER 3. PART I: SEMI-CLASSICAL SOLUTIONS FOR THE DIRAC EQUATION. PART II: SEMI-CLASSICAL EQUATION OF MOTION FOR A RADIATING ELECTRON.

Descriptive Note : Rept. for 15 Sep 63-15 Sep 66,

Corporate Author : STEVENS INST OF TECH HOBOKEN NJ DEPT OF PHYSICS AND ENGINEERING PHYSICS

Personal Author(s) : Rosen, Bernard

Report Date : 01 NOV 1966

Pagination or Media Count : 39

Abstract : The solution of Dirac's equation by the use of the semi-classical approximation is discussed. Discussions are given for a Dirac particle in: the field of an electromagnetic plane wave; the field of an e.m. plane wave plus a static magnetic field propagation; and the Coulomb field. An equation of motion for a radiating electron is calculated using certain results from quantum electrodynamics. Use is made of the fact that the charge density for a point electron is not completely localized. The resulting equation contains Planck's constant and reduces, in the limit approaches zero, to the usual equation, that is, the one containing a third derivative of the displacement with respect to time. This equation does not possess runaway solutions if the mechanical mass is greater than zero. This is a special case of the Widermuth-Herglotz theorem. The equation derived does not satisfactorily handle the case of a stepforce. The general problem of attempting to construct a linear equation that will correctly describe radiation-reaction is discussed.

Descriptors :   (*FIELD THEORY, APPROXIMATION(MATHEMATICS)), ELECTROMAGNETIC FIELDS, WAVE FUNCTIONS, WAVE PROPAGATION, ELECTROMAGNETIC RADIATION, PROPAGATION, MAGNETIC FIELDS, DIFFERENTIAL EQUATIONS, ELECTRONS, EQUATIONS OF MOTION, ELECTRON DENSITY, INTEGRAL EQUATIONS, INTEGRAL TRANSFORMS.

Subject Categories : Electricity and Magnetism

Distribution Statement : APPROVED FOR PUBLIC RELEASE