On Solutions of an Equation of Transfer for a Planetary Atmosphere
Abstract
A set of general solutions to the homogeneous vector equation of transfer for the two azimuthinde pendent components of a partially planepolarized radiation field is obtained. In addition to describing the scattering of light by anisotropic particles, the model considered here is appropriate for the quantum theory of resonance line scattering. The analysis, which is based on Case's method of normal modes, yields two discrete eigenvectors and two linearly independent, degenerate, singular, continuum eigen vectors. A fullrange completeness theorem for the aforementioned eigenvectors is proved by solving two coupled singular integral equations. Further, a fullrange orthogonality theorem is proved, the necessary normalization integrals are determined, and the fullrange adjoint vectors are constructed
 Publication:

The Astrophysical Journal
 Pub Date:
 February 1969
 DOI:
 10.1086/149891
 Bibcode:
 1969ApJ...155..555M