Multipole expansions in four-dimensional hyperspherical harmonics

By Alexei V. Meremianin. 2005

18 citations recorded by the source corpus.

The technique of vector differentiation is applied to the problem of the derivation of multipole expansions in four-dimensional space. Explicit expressions for the multipole expansion of the function with r = r1 + r2 are given in terms of tensor products of two hyperspherical harmonics depending on the unit vectors and . The multipole decomposition of the function (r1 r2)n is also derived. The proposed method can be easily generalized to the case of the space with dimensionality larger than four. Several explicit expressions for the four-dimensional Clebsch–Gordan coefficients with particular values of parameters are presented in the closed form.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials (2014, background): “The coupling coefficients are non-zero only for non-negative integer and half-integer values of j1, j2, and j satisfying the conditions ‖j1 − j2‖ ≤ j ≤ j1 + j2 and j1 + j2− j not half-integer [9].”