ELECTRIC DIPOLE APPROXIMATION AND THE CANONICAL FORMALISM IN ELECTRODYNAMICS

Journal Article · Fri Sep 01 00:00:00 EDT 1961 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.123.1903· OSTI ID:4839461

Schwartz, M

The electric dipole approximation is used to study the problem of finding commuting solutions of coupled equations of motion. It is pointed out that for a charged particle in an external radiation field, the solutions of the coupled equations cannot be considered independent in the sense of commuting with one another if the homogeneous solutions are assumed to have the commutation properties of uncoupled variables. The case of a charged free particle and a charged harmonic oscillator in an external radiation field is explicitly treated. It is indicated that for a retarded (advanced) self-field, the free particle fits into a canonical formalism while the oscillator does not. For a stationary self- field, both the free particle and the oscillator fit into a canonical formalism. It is shown that the Fourier transforms of the configuration space solutions (based on e/sup ik-//sup x/ and e/sup i /sup mt/) do not exist. In the latter connec- tion, it is pointed out that earlier treatments of the oscillator by Sokolov and Tumanov and Norton and Watson contain misleading results as a consequence of their using Fourier transforms. (auth)

• Research Organization: Syracuse Univ., N.Y.
• NSA Number: NSA-15-031778
• OSTI ID: 4839461
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 123; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

CHARGED PARTICLES
DIPOLES
ELECTRODYNAMICS
EQUATIONS
FOURIER ANALYSIS
MATHEMATICS
MOTION
OSCILLATIONS
PHYSICS