Harmonic polynomials, hyperspherical harmonics, and atomic spectra. (English) Zbl 1188.33013

A study of the properties of homogeneous and harmonic polynomials offers an alternative approach to the theory of hyperspherical harmonics. For instance, the hyperangular integral can be evaluated by group theoretical methods, as has been shown by Aquilanti and Caligiana. However, the theorems discussed in the present paper suggest an alternative and easy way to compute this integral. So, the methods discussed in the paper should be thought of as complementary to the group theory. These mathematical considerations have important physical applications because both Sturmians and generalized Sturmians have shown to be extremely useful in the quantum theory of atoms.


33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)


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