Abstract
Spherical harmonics play an important role in electrodynamics and in quantum mechanics. We shall show how they appear in the representation theory of the rotation group SO(3). Each irreducible representation of SO(3) can be realized in a finite-dimensional Hilbert space of functions on the sphere, the restrictions of harmonic homogeneous polynomials of a given degree, and this representation is unitary.
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Notes
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I found such a sketch by Stephen Wolfram on his web page and I recommend it.
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Kosmann-Schwarzbach, Y. (2022). Spherical Harmonics. In: Groups and Symmetries. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-030-94360-8_7
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DOI: https://doi.org/10.1007/978-3-030-94360-8_7
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Online ISBN: 978-3-030-94360-8
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