Abstract
Helmholtz' solid harmonics (spherical Bessel functions × spherical surface harmonics) are generated from fundamental spherical waves through a ladder procedure using raising and lowering operators. The addition theorem for them and the bipolar expansion formula of a screened Coulomb potential are derived. A method for evaluating two-center integrals with a general potential is given in the last section. This is new and useful in practical calculations. A key function Jlnm(x)=12 ∫ −11 dμ eiμxPlm(μ)Pnm(μ),which appears in all the essential results, is studied in detail.
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