Table of spherical harmonics
This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree l = 10. Some of these formulas give the "Cartesian" version. This assumes x, y, z, and r are related to and through the usual spherical-to-Cartesian coordinate transformation:
Spherical harmonics
l = 0[1]
l = 1[1]
l = 2[1]
l = 3[1]
l = 4[1]
l = 5[1]
l = 6
l = 7
l = 8
l = 9
l = 10
Real spherical harmonics
For each real spherical harmonic, the corresponding atomic orbital symbol (s, p, d, f, g) is reported as well.
l = 0[2][3]
l = 1[2][3]
l = 2[2][3]
l = 3[2]
l = 4
See also
External links
References
- Cited references
- 1 2 3 4 5 6 D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii (1988). Quantum theory of angular momentum : irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols (1. repr. ed.). Singapore: World Scientific Pub. p. 155-156. ISBN 9971-50-107-4.
- 1 2 3 4 C.D.H. Chisholm (1976). Group theoretical techniques in quantum chemistry. New York: Academic Press. ISBN 0-12-172950-8.
- 1 2 3 Blanco, Miguel A.; Flórez, M.; Bermejo, M. (1 December 1997). "Evaluation of the rotation matrices in the basis of real spherical harmonics". Journal of Molecular Structure: THEOCHEM 419 (1–3): 19–27. doi:10.1016/S0166-1280(97)00185-1.
- General references
- See section 3 in Mathar, R. J. (2009). "Zernike basis to cartesian transformations". Serbian Astronomical Journal 179 (179): 107–120. arXiv:0809.2368. Bibcode:2009SerAj.179..107M. doi:10.2298/SAJ0979107M. (see section 3.3)
- For complex spherical harmonics, see also SphericalHarmonicY[l,m,theta,phi] at Wolfram Alpha, especially for specific values of l and m.
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