Spherical wave functions translation addition theorem

O. Cruzan, Translational addition theorems for spherical vector wave functions. Q. Appl. Math. 20 (1), 33 0 (1962)... 

In this case the interacting held is the image of the scattered field and the expansion (2.198) can be derived by using the addition theorem for vector spherical wave functions. The elements of the reflection matrix are the translation coefficients, and as a result, the amount of computer time required to solve the scattering problem is significantly reduced. In this regard it should... 

In general, the translation addition theorem for vector spherical wave functions can be written as [43,213]... 

This volume is intended for engineering and physics students as well as researchers in scattering theory, and therefore we decided to leave out rigorous mathematical details. The properties of scalar and vector spherical wave functions, addition theorems under translation and rotation of the coordinate systems and some completeness results are presented in appendices. These can be regarded as a collection of necessary formulas. 

For a system of Af particles with o = f3i = 7 = 0, I = 1,2,. ..,AA, the transformations of the vector spherical vector wave functions involve only the addition theorem under coordinate translations, i.e.,... 

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