Group Representations I: Rotations and Spherical Harmonics
In this chapter and the next two, three apparently remote subjects are shown to have important interconnections: group representations, the classical special functions, and quantum mechanics.
KeywordsRepresentation faithful representation dimension reducibility irreducible representation tensor transformation laws representations of SO(2) and SO(3) infinitesimal operators raising and lowering operators effective and transitive action of a group homogeneous space regular representation tesseral harmonics Legendre polynomials and associated Legendre functions recurrence relations and the differential equation for Plm Rodrigues’ formula for Plm orthonormality and completeness of the tesseral harmonics addition theorem
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