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A SIMPLE DERIVATION OF THE WIGNER-ECKART THEOREM

Huang Shi-zhong

Based on the commutation relations between the components of an irreducible tensor operator of rank k and the angular momentum operator, a simple derivation of the Wigner-Eckart theorem is presented with the aid of the properties of angular momentum operators and their eigenstates.

Journal of Anhui Normal UniversityJan 1, 20030 citations

Addition of Angular Momenta— The Wigner—Eckart Theorem

Arno Böhm, Mark E. Loewe

Springer eBooksJan 1, 19930 citations

Proof of the Wigner-Eckart Theorem

Springer eBooksJul 4, 20070 citations

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

R. Simon, Narasimhaiengar Mukunda, S. Chaturvedi +1 more

arXiv:0808.0779Physics Letters AOct 10, 200828 citations

The Wigner–Eckart Theorem and Other Applications

Nadir Jeevanjee

Chapter 6 applies the material of the previous chapters to some particular topics, specifically the Wigner–Eckart theorem, selection rules, and gamma matrices and Dirac bilinears. We begin by discussing the perennially confusing concepts of vector operators and spherical tensors, and then unify them using the notion of a representation operator. We then use this framework to derive a generalized selection rule, from which the various quantum-mechanical selection rules can be derived, and we also discuss the Wigner–Eckart theorem. We conclude by showing that Dirac’s famous gamma matrices can be understood in terms of representation operators, which then immediately gives the transformation properties of the ‘Dirac bilinears’ of QED.Chapter 6 applies the material of the previous chapters to some particular topics, specifically the Wigner–Eckart theorem, selection rules, and gamma matrices and Dirac bilinears. We begin by discussing the perennially confusing concepts of vector operators and spherical tensors, and then unify them using the notion of a representation operator. We then use this framework to derive a generalized selection rule, from which the various quantum-mechanical selection rules can be derived, and we also discuss the Wigner–Eckart theorem. We conclude by showing that Dirac’s famous gamma matrices can be understood in terms of representation operators, which then immediately gives the transformation properties of the ‘Dirac bilinears’ of QED.

Birkhäuser Boston eBooksJan 1, 20110 citations

An alternative proof of Wigner theorem on quantum transformations based on elementary complex analysis

Amaury Mouchet

arXiv:1304.1376Physics Letters AAug 26, 201310 citations

Adapted Wigner–Eckart theorem

Abstract

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Adapted Wigner–Eckart theorem

Abstract

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