Solutions of the Maxwell equations and photon wave functions

Journal Article · Mon Mar 15 00:00:00 EDT 2010 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2009.11.007· OSTI ID:21336109

Mohr, Peter J. ^[1]

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1. National Institute of Standards and Technology, Gaithersburg, MD 20899-8420 (United States), E-mail: [e-mail]

Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including sources, is invariant under Lorentz transformations. Complete sets of eigenfunctions of the Hamiltonian for the electromagnetic fields, which may be interpreted as photon wave functions, are given both for plane waves and for angular-momentum eigenstates. Rotationally invariant projection operators are used to identify transverse or longitudinal electric and magnetic fields. For plane waves, the velocity transformed transverse wave functions are also transverse, and the velocity transformed longitudinal wave functions include both longitudinal and transverse components. A suitable sum over these eigenfunctions provides a Green function for the matrix Maxwell equation, which can be expressed in the same covariant form as the Green function for the Dirac equation. Radiation from a dipole source and from a Dirac atomic transition current are calculated to illustrate applications of the Maxwell Green function.

• OSTI ID: 21336109
• Journal Information: Annals of Physics (New York), Vol. 325, Issue 3; Other Information: DOI: 10.1016/j.aop.2009.11.007; PII: S0003-4916(09)00225-5; Copyright (c) 2009 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
ANGULAR MOMENTUM
DIPOLES
DIRAC EQUATION
EIGENFUNCTIONS
EIGENSTATES
ELECTROMAGNETIC FIELDS
GREEN FUNCTION
HAMILTONIANS
LORENTZ TRANSFORMATIONS
MAGNETIC FIELDS
MATRICES
MAXWELL EQUATIONS
PHOTONS
PROJECTION OPERATORS
VELOCITY
WAVE FUNCTIONS
WAVE PROPAGATION