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- *''See [[Spherical harmonics/Catalogs]] for a table of spherical harmonics through ℓ'' = 4. '''Spherical harmonics''' are functions arising in [[physics]] and [[mathematics]] when [[spheric34 KB (5,282 words) - 14:21, 1 January 2011
- 150 bytes (22 words) - 13:28, 2 September 2008
- 35 bytes (3 words) - 21:59, 25 October 2009
- ==First few spherical harmonics==3 KB (444 words) - 06:07, 9 September 2009
- 12 bytes (1 word) - 20:10, 14 November 2007
- | title = An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them | title = Spherical Harmonics2 KB (249 words) - 09:50, 13 September 2009
- 631 bytes (84 words) - 06:48, 31 January 2009
Page text matches
- #REDIRECT [[spherical harmonics]]33 bytes (3 words) - 11:48, 4 September 2007
- | title = An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them | title = Spherical Harmonics873 bytes (109 words) - 09:50, 13 September 2009
- | title = An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them | title = Spherical Harmonics2 KB (249 words) - 09:50, 13 September 2009
- {{r|Spherical harmonics}}1,006 bytes (129 words) - 20:33, 11 January 2010
- {{r|Spherical harmonics}}702 bytes (87 words) - 20:28, 11 January 2010
- The function <math>Y^m_{\ell}</math> is a normalized [[spherical harmonics|spherical harmonic function]]. The expansion takes a simpler form when wri Use of the [[Spherical harmonics#Spherical harmonic addition theorem|spherical harmonic addition theorem]]3 KB (409 words) - 00:52, 4 June 2009
- {{r|Spherical harmonics}}876 bytes (107 words) - 10:56, 11 January 2010
- {{r|Spherical harmonics}}879 bytes (114 words) - 03:09, 8 March 2024
- {{r|Spherical harmonics}}965 bytes (124 words) - 17:23, 11 January 2010
- {{r|Spherical harmonics}}1 KB (154 words) - 07:04, 30 July 2008
- {{r|Spherical harmonics}}1 KB (157 words) - 19:35, 11 January 2010
- {{r|Spherical harmonics}}468 bytes (58 words) - 07:36, 8 January 2010
- ==First few spherical harmonics==3 KB (444 words) - 06:07, 9 September 2009
- {{r|Spherical harmonics}}572 bytes (74 words) - 21:40, 11 January 2010
- {{r|Spherical harmonics}}638 bytes (78 words) - 18:02, 11 January 2010
- {{r|Spherical harmonics}}665 bytes (92 words) - 09:00, 15 July 2008
- {{r|Spherical harmonics}}1 KB (216 words) - 05:25, 20 April 2010
- {{r|Spherical harmonics}}762 bytes (99 words) - 17:00, 11 January 2010
- ...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 [[spher5 KB (822 words) - 17:36, 14 November 2007
- ...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<sup> ''l''</sup>). Both functions are not normalized to unity, but12 KB (1,953 words) - 04:38, 5 October 2009
- 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 ==16 KB (2,612 words) - 09:02, 9 February 2010
- {{r|Spherical harmonics}}1 KB (166 words) - 11:15, 24 December 2010
- ....g. [[gyrification]]) or overall shape (e.g. via [[spherical wavelets]], [[spherical harmonics]] or [[Laplace-Beltrami spectra]]).3 KB (440 words) - 08:31, 1 March 2024
- ...ons]], <math>J_n(r)</math>, and the solutions for <math>Y</math> are the [[spherical harmonics]], <math>Y_{lm}(\theta,\phi)</math>.8 KB (1,340 words) - 07:25, 27 October 2007
- *''See [[Spherical harmonics/Catalogs]] for a table of spherical harmonics through ℓ'' = 4. '''Spherical harmonics''' are functions arising in [[physics]] and [[mathematics]] when [[spheric34 KB (5,282 words) - 14:21, 1 January 2011
- 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 δ's are [[Kronecker delta]]s (zero if th8 KB (1,273 words) - 11:29, 9 July 2009
- ...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).10 KB (1,514 words) - 19:38, 20 November 2009
- to [[spherical harmonics]], normalized to unity and with Condon and Shortley phase convention,11 KB (1,671 words) - 06:37, 1 November 2009
- In more advanced treatises—also American—on [[spherical harmonics|spherical functions]] the old convention remains in use, see e.g. Miller<re27 KB (4,267 words) - 10:14, 8 April 2023
- ...n. It is common to choose [[solid harmonic]] functions (which differ from spherical harmonics only by a factor ''r''<sub>A1</sub><sup> ''l''</sup> ) 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.14 KB (2,265 words) - 05:37, 6 March 2024
- == 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 pos16 KB (2,523 words) - 03:58, 21 January 2009
- In [[Solid harmonics#Derivation, relation to spherical harmonics|this article]] (in which ''l''<sup> 2 </sup> is defined without Planck's co where ''Y''<sub>''lm''</sub> are [[spherical harmonics]], which are eigenfunctions of ''l''<sup> 2</sup> with eigenvalues <math>{\19 KB (2,981 words) - 18:31, 3 November 2021
- According to Ferrers<ref> N. M. Ferrers, ''An Elementary Treatise on Spherical Harmonics'', MacMillan, 1877 (London), p. 77. [http://www.archive.org/stream/element7 KB (1,150 words) - 07:58, 24 January 2010
- ...pace with an odd number of dimensions (2ℓ+1) can be constructed from the [[spherical harmonics]] ''Y''<sub>ℓ</sub><sup>m</sup>, 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}}20 KB (3,045 words) - 11:21, 29 June 2011
- ...the nineteenth century, long before quantum mechanics was born. They are [[Spherical harmonics#Eigenfunctions of orbital angular momentum|spherical harmonic functions]].16 KB (2,632 words) - 04:33, 23 September 2021
- ...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>{\scr20 KB (3,081 words) - 21:57, 31 March 2022