Special functions defined on the surface of a sphere, often employed in solving partial differential equations. They form a complete set of orthogonal functions and thus an orthonormal basis.
Questions tagged [spherical-harmonics]
287 questions
3
votes
0 answers
The product of three spherical harmonics in higher dimension
As I see, e.g., in this question, a closed formula for the following integral
\begin{equation}
\int_{\mathbb{S}^N} Y_{\ell_1\ldots \ell_N}\,Y_{\ell'_1\ldots\ell'_N}\,Y_{\ell''_1\ldots \ell''_N}\, d^N S
\end{equation}
is well-known in the $N=2$…
Giuseppe Negro
- 767
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- 21
3
votes
2 answers
Harmonics on Hyperbolic space
I would like to know if there exists an analogue for hyperbolic space of the so called spherical harmonics which play a major role in the quantum states construction in a hydrogen atom. In other words are there 'hyperbolic harmonics' and how trivial…
Cala
- 437
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vote
0 answers
Integral of spherical harmonics and their derivatives
What is the Integral of the product of spherical harmonics and derivatives of spherical harmonics? More precisely, I am looking for
$$\int_\Omega d\Omega\, Y_{l}^m Y_{l^\prime}^{m^\prime} \partial_\theta…
Fluid
- 21
0
votes
0 answers
How could I calculate the product of two spherical harmonics
For now I have to calculate the product of two spin-weighted spherical harmonics:
$ _{s}Y_{lm}\ \times\ _{s}Y_{lm}^{*}$
What’s the result of this product? Maybe it is a spin-weighted 0 spherical harmonics with some coefficients?
Horjsib
- 1