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{{r|Spherical harmonics}}

...nics]] as the angular part of the Slater orbital. A list of Cartesian real spherical harmonics is given in this [[solid harmonics|article]]. ...'' = 2. Functions between square brackets in the list are normalized real spherical harmonics. These functions are given in Cartesian form but, when expressed in [[spher

...areful with hbar, I'm a bit sloppy with it. I'm working on an article on [[spherical harmonics]] right now and there I specifically stated that I take hbar = 1. Maybe you It is [[Angular momentum#Relation to spherical harmonics|known]] that [[spherical harmonics]] Y^m_l are eigenfunctions <math>(\mathbf{r} \times \n

...ch has the advantage that no prerequisite knowledge of Legendre functions, spherical harmonics, etc., is assumed. Its disadvantage is that the derivations are fairly cumb ...) and <math>R^m_{\ell}(\mathbf{r})</math> is a regular solid harmonics (a spherical harmonics times r^''l''). Both functions are not normalized to unity, but

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]]).

...aph of the article itself is to theoretical. How about incorporating the [[Spherical harmonics/Definition]] into the first few sentences of the article? -- [[User:Alexand the kets ''| j, m >'' are nothing but the spherical harmonics <math>Y^m_\ell</math> (the subject of the article) and the ''J'' operators

...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).

== Spherical harmonics == Hi Fredrik, some time ago you commented that the article [[spherical harmonics]] could do with some drawings. I would appreciate it if you have any sugges

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

{{rpl|Spherical harmonics}}

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...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>{\