The Green's function for the three-dimensional linear Boltzmann equation via Fourier transform

TL;DR

This paper extends the computation of the Green's function for the 3D linear Boltzmann equation using Fourier transforms to include arbitrary anisotropic scattering, broadening its applicability beyond isotropic cases.

Contribution

It demonstrates that the Fourier transform method for calculating the Green's function applies to anisotropic scattering, not just isotropic, in three-dimensional space.

Findings

Green's function computed via Fourier transform for anisotropic scattering

Method applicable in three-dimensional infinite space

Broadens understanding of scattering processes in Boltzmann equation

Abstract

The linear Boltzmann equation with constant coefficients in the three-dimensional infinite space is revisited. It is known that the Green's function can be calculated via the Fourier transform in the case of isotropic scattering. In this paper, we show that the three-dimensional Green's function can be computed with the Fourier transform even in the case of arbitrary anisotropic scattering.