Expansion about an Arbitrary Point of Three-Dimensional Functions Involving Spherical Harmonics by the Fourier-Transform Convolution Theorem

Publisher Website
Google Scholar
Abstract
Expansion of ψ(r)=ψ(r)YLM(θ,φ) in terms of spherical harmonics and radial functions, whose coordinates are measured from an arbitrary point in space, is obtained by use of the Fourier-transform convolution theorem. For a specific ψ(r), two integrals most be evaluated to determine the expansion explicitly: (1) the radial part ψ̄(k) of the Fourier transform of ψ(r); and (2) an integral of ψ̄(k) with spherical Bessel functions. The examples of noninteger-n and integer-n Slater-type orbitals are worked out by contour integration.