Abstract
Now that we have seen how wave functions and state vectors are changed under symmetry operations, it is natural to ask how operators are transformed under the same operations.
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Notes
- 1.
See, for example, A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, N. J.,1960), Chap. 3.
- 2.
The rotation matrices Ṟ\(\left ( \alpha ,\beta ,\gamma \right ) \) form a group of orthogonal 3 × 3 matrices having determinant equal to + 1, a group that is refered to as the special orthogonal group in three dimensions, SO(3). The group of unitary 2 × 2 matrices having determinant equal to + 1, such as the \(\mathcal {D}^{(1/2)}\left ( \alpha ,\beta ,\gamma \right ) \) matrices, is refered to as the special unitary group in two dimensions, SU(2).
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Berman, P.R. (2018). Addition of Angular Momenta, Clebsch-Gordan Coefficients, Vector and Tensor Operators, Wigner-Eckart Theorem. In: Introductory Quantum Mechanics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-68598-4_20
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DOI: https://doi.org/10.1007/978-3-319-68598-4_20
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