Editing Spherical harmonics
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The '''spherical harmonics''' <math>Y_l^m (\theta,\phi)</math> are the angular portion of the solution to [[Laplace's equation]] in spherical coordinates. | The '''spherical harmonics''' <math>Y_l^m (\theta,\phi)</math> are the angular portion of the solution to [[Laplace's equation]] in spherical coordinates. | ||
The first few spherical harmonics are given by: | The first few spherical harmonics are given by: | ||
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:<math>Y_1^1 (\theta,\phi) = -\frac{1}{2} \sqrt{\frac{3}{2\pi}} \sin \theta e^{i\phi} </math> | :<math>Y_1^1 (\theta,\phi) = -\frac{1}{2} \sqrt{\frac{3}{2\pi}} \sin \theta e^{i\phi} </math> | ||
==See also== | ==See also== | ||
* | *M. E. Rose "Elementary theory of angular momentum", John Wiley & Sons (1967) Appendix III | ||
*[http://mathworld.wolfram.com/SphericalHarmonic.html Spherical Harmonic -- from Wolfram MathWorld] | *[http://mathworld.wolfram.com/SphericalHarmonic.html Spherical Harmonic -- from Wolfram MathWorld] | ||
*[http://dx.doi.org/10.1007/BF01597437 I. Nezbeda, J. Kolafa and S. Labík "The spherical harmonic expansion coefficients and multidimensional integrals in theories of liquids", Czechoslovak Journal of Physics '''39''' pp. 65-79 (1989)] | *[http://dx.doi.org/10.1007/BF01597437 I. Nezbeda, J. Kolafa and S. Labík "The spherical harmonic expansion coefficients and multidimensional integrals in theories of liquids", Czechoslovak Journal of Physics '''39''' pp. 65-79 (1989)] | ||
[[category: mathematics]] | [[category: mathematics]] |