An alternative expression for the addition theorems of spherical wave solutions of the Helmholtz equation

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Abstract

An alternative formulation of the addition theorem for spherical wave solutions of the Helmholtz equation is presented. The 3-j symbols of Wigner, or more precisely the Gaunt coefficient (complete solid angle integral of a triple product of spherical harmonics), which appear in the formerly introduced expressions of these addition theorems are replaced by an explicit matrix expression relating the spherical wave solutions defined with respect to the different origins. The generalized Gaunt coefficients, which are complete solid angle integrals of a multiple product of spherical harmonics, can then be written in terms of a matrix product of basic matrices representing the Gaunt coefficient.
Original languageEnglish
Pages (from-to)5292-5302
Number of pages11
JournalJournal of Mathematical Physics
Volume34
Issue number11
DOIs
Publication statusPublished - 1993

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