Wigner-Eckart theorem


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Wigner-Eckart theorem

[′wig·nər ′ek·ərt ‚thir·əm]
(quantum mechanics)
A theorem in the quantum theory of angular momentum which states that the matrix elements of a tensor operator can be factored into two quantities, the first of which is a vector-coupling coefficient, and the second of which contains the information about the physical properties of the particular states and operator, and is completely independent of the magnetic quantum numbers.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
By using (3) and (4) and applying the Wigner-Eckart theorem the matrix element of the Hamiltonian [H.sub.[gamma]] can take the following form:
In this paper, f-f MD transition in rare-earth doped crystals is investigated and general expressions of magnetic permeability are derived according to semi-classic theory and Wigner-Eckart theorem. As an example, the EM parameters of [Sm.sup.3+] and [Yb.sup.3+] co-doped [Y.sub.3][Al.sub.5][O.sub.12] (abbreviated as YAG) crystal are calculated numerically, and a frequency band with negative refractive index is observed.
The Wigner-Eckart theorem shows that (6) can be cast into a product of a Wigner 3j symbol and a reduced matrix element [10, see p.