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Both kinds of solid harmonics are simply related to [[spherical harmonics]] <math>\scriptstyle Y^m_\ell</math> (normalized to unity), == Derivation, relation to spherical harmonics ==

{{r|Spherical harmonics}}

....g. [[gyrification]]) or overall shape (e.g. via [[spherical wavelets]], [[spherical harmonics]] or [[Laplace-Beltrami spectra]]).

...ons]], <math>J_n(r)</math>, and the solutions for <math>Y</math> are the [[spherical harmonics]], <math>Y_{lm}(\theta,\phi)</math>.

*''See [[Spherical harmonics/Catalogs]] for a table of spherical harmonics through ℓ'' = 4. '''Spherical harmonics''' are functions arising in [[physics]] and [[mathematics]] when [[spheric

It can be shown that [[spherical harmonics]] are eigenvectors of both commuting operators simultaneously Here <math>N_{\ell}^m</math> is a normalization constant (for spherical harmonics usually equal unity) and the &delta;'s are [[Kronecker delta]]s (zero if th

...nly plotted. The angular parts of atomic orbitals are functions known as [[spherical harmonics]]. ...nctions and hence they have the same appearance as these functions. (See [[spherical harmonics]] for a few graphical illustrations).

to [[spherical harmonics]], normalized to unity and with Condon and Shortley phase convention,

In more advanced treatises&mdash;also American&mdash;on [[spherical harmonics|spherical functions]] the old convention remains in use, see e.g. Miller<re

...n. It is common to choose [[solid harmonic]] functions (which differ from spherical harmonics only by a factor ''r''_A1^''l'' ) as the angular parts ...en-like atom. The angular parts, however, are the same analytic functions (spherical harmonics) as in the case of the hydrogen-like-atom.

== Netherlands and spherical harmonics == I saw two of my articles: [[The Netherlands]] and [[Spherical harmonics]] in the list. I gave both a checklist quite some time ago. How is that pos

In [[Solid harmonics#Derivation, relation to spherical harmonics|this article]] (in which ''l''² is defined without Planck's co where ''Y''_''lm'' are [[spherical harmonics]], which are eigenfunctions of ''l''² with eigenvalues <math>{\

According to Ferrers<ref> N. M. Ferrers, ''An Elementary Treatise on Spherical Harmonics'', MacMillan, 1877 (London), p. 77. [http://www.archive.org/stream/element

...pace with an odd number of dimensions (2ℓ+1) can be constructed from the [[spherical harmonics]] ''Y''_ℓ^m, and their transformations under infinite ...ogle.com/books?id=25eTtXqLW8UC&pg=PA83 |pages=pp. 83''ff'' |chapter=§3.3.2 Spherical harmonics |isbn=0387986472 |year=1999 |publisher=Springer}}

...the nineteenth century, long before quantum mechanics was born. They are [[Spherical harmonics#Eigenfunctions of orbital angular momentum|spherical harmonic functions]].

...r|known]] that the rotational wave functions of a linear rigid rotor are [[spherical harmonics]] <math>{\scriptstyle Y_\ell^m(\hat{\mathbf{r}})}</math>, where <math>{\scr