Recall as you read this that and in addition to the treatment of this available in Jackson, chapters 2, 3, 6, and 8 of Wyld, and doubtless Arfkin, Morse and Feshback, and probably six other sources if you look. Very important stuff, can't know it too well.

Recall from above the **Homogeneous Helmholtz Equation** (HHE):

(13.12) |

We assume that

(13.13) |

We reduce the HHE with this assumption to the

(13.14) |

If we substitute

(13.15) |

we transform this into an equation for ,

(13.16) |

The is

Two linearly independent solutions on
minus the origin to this
radial DE are:

(13.17) | |||

(13.18) |

the

The following is a **MINIMAL** table of their important properties.
A better table can be found in Wyld between chps. 6 and 7 and in Morse
and Feshbach (I can't remember which volume).

- Properties of Spherical Bessel Functions

- , , and )
- General Solutions to the HHE
- Green's Functions and Free Spherical Waves