Interior and exterior spherical basis solutions
(solutions of the Helmholtz-equation in spherical coordinates)
Interior solution
The interior solution must stay finite for all radii r![spherical basis-solution for interior fields spherical basis-solution for interior fields](https://iaem.at/Members/zotter/spherical_soundfield/sh_rad_incoming.gif)
Exterior solution
The exterior solution must fulfill a harder constraint: the Sommerfeld radiation condition. If the function diverges near r=0, this is can be accepted. However, far-enough away, the solutions must decay with 1/r and their phase propagation must accord to the free-field wave length.![spherical basis-solution for radiation spherical basis-solution for radiation](https://iaem.at/Members/zotter/spherical_soundfield/sh_rad.gif)