Physics – Mathematical Physics
Scientific paper
2005-10-24
J. Phys. A, vol. 39, p.3099, 2006
Physics
Mathematical Physics
19 pages, no figures
Scientific paper
10.1088/0305-4470/39/12/017
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 $r^n C_j (\hr)$ with $\vvr=\vvr_1+\vvr_2$ are given in terms of tensor products of two hyperspherical harmonics depending on the unit vectors $\hr_1$ and $\hr_2$. The multipole decomposition of the function $(\vvr_1 \cdot \vvr_2)^n$ is also derived. The proposed method can be easily generalised 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.
No associations
LandOfFree
Multipole expansions in four-dimensional hyperspherical harmonics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Multipole expansions in four-dimensional hyperspherical harmonics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multipole expansions in four-dimensional hyperspherical harmonics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-522860