WebOct 15, 2024 · There are a variety of alternative spherical harmonic systems. For example, spherical harmonic systems can be formulated in quaternion representation (see, e.g., K. Gürlebeck, W. Sprösig (2015)). Spherical harmonics may be generated in the framework of... WebJun 9, 2024 · The usual spherical harmonics can be defined from Laplace’s equations \(\nabla ^{2}f=0\) as solutions in the two angular coordinates of a sphere once a point on the sphere has been selected to serve as the North pole. As we have mentioned before, the spin-weighted spherical harmonics are generalizations of the standard spherical harmonics, …
Spin‐ s Spherical Harmonics and ð - AIP Publishing
WebMay 3, 2024 · The reason is this: spherical harmonics are the eigen functions of the angular momentum operator (in the quantum view), meaning they are the standing wave solutions to waves on a sphere (in the classical view), and those are easy to visualize. WebOct 1, 2024 · The spin-weighted spherical harmonics (by Newman and Penrose) form an orthonormal basis of L2(Ω) on the unit sphere Ω and have a huge field of applications. ibooks for ipad pro
How should spin-weighted spherical functions be defined?
WebThe spherical harmonics Ymℓ (θ, ϕ) are functions of two angles, θ and ϕ. They are defined by taking the associated Legendre functions Pmℓ (cosθ), which depend on θ only, and multiplying them by. eimϕ = cos(mϕ) + isin(mϕ), a complex function of the second angle. WebApr 27, 2016 · Here, it is proposed that spin-weighted spherical functions should be treated as functions on the spin group. This approach more cleanly reflects the geometry … WebThe spherical harmonics can be defined in various ways; they are eigenfunctions of the Laplace-Beltrami operator of the sphere and they are the angular part of the separable solutions in spherical coordinates of the Laplace equation in Euclidean space. Another useful characterization is given by the following result. Keywords Spherical Harmonic ibooks for ipad