Double Spherical Harmonics Method in Spherical Geometries.

摘要

The spherical Milne'problem.is treated by a modification of the spherical harmonics method in which different Legendre expansions are employed in the forward and backward directions (Yvon' s modification). It is found that the resulting system of differential equations has no solution, and it can be evaluated only with the help of additional considerations, which however tend to decrease the quality of the approximation considerably. The calculations are carried out in detail in the Pi2- approximation, and the results 'compared with those found by other methods. It is concluded that the double spherical harmonics method in spherical geometries in unsuited for numerical calculations.