Abstract
Classically, angular momentum may be thought of as the Hamiltonian generator of rotations (Proposition 2.30). Angular momentum is a particularly useful concept when a system has rotational symmetry, since in that case the angular momentum is a conserved quantity (Proposition 2.18). Quantum mechanically, angular momentum is still the “generator”of rotations, meaning that it is the infinitesimal generator of a one-parameter group of unitary rotation operators, in the sense of Stone’s theorem (Theorem 10.15).
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References
G.B. Folland, A Course in Abstract Harmonic Analysis (CRC Press, Boca Raton, FL, 1995)
B.C. Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction. Graduate Texts in Mathematics, vol. 222 (Springer, New York, 2003)
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Hall, B.C. (2013). Angular Momentum and Spin. In: Quantum Theory for Mathematicians. Graduate Texts in Mathematics, vol 267. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7116-5_17
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DOI: https://doi.org/10.1007/978-1-4614-7116-5_17
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