Singular eigenfunctions for the three-dimensional radiative transport equation

TL;DR

This paper extends Case's method to find elementary solutions for the three-dimensional radiative transport equation, where the specific intensity depends on three spatial variables, by linking to singular eigenfunctions of the one-dimensional case.

Contribution

The paper generalizes Case's method to three-dimensional space, connecting solutions to singular eigenfunctions of the one-dimensional radiative transport equation.

Findings

Elementary solutions depend on three spatial variables.

Angular part linked to singular eigenfunctions.

Method generalizes previous one-dimensional solutions.

Abstract

Case's method obtains solutions to the radiative transport equation as superpositions of elementary solutions when the specific intensity depends on one spatial variable. In this paper, we find elementary solutions when the specific intensity depends on three spatial variables in three-dimensional space. By using the reference frame whose z-axis lies in the direction of the wave vector, the angular part of each elementary solution becomes the singular eigenfunction for the one-dimensional radiative transport equation. Thus Case's method is generalized.