In vector calculus, the "'curl "'is a vector operator that describes the vector.
2.
Central to these distinctions is the fact that del is not simply a vector; it is a vector operator.
3.
Where " ? ijk " is the Levi-Civita symbol, which all vector operators must satisfy, by construction.
4.
The bold-face vectors with circumflexes are not unit vectors, they are 3-vector operators; all three spatial components taken together.
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When stated another way, one can say that the Wigner Eckart theorem is a theorem that tells you how vector operators behave in a subspace.
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Within a given subspace, a component of a vector operator will behave in a way proportional to the same component of the angular momentum operator.
7.
Vector operator notation will be used, in particular " is gradient, " ?" is divergence, and " ?is curl.
8.
The triple is a vector operator and the Wigner & ndash; Eckart theorem applies for computation of matrix elements between the states represented by the chosen basis.
9.
Of the vector operators the cross product cannot be used in six dimensions; instead the wedge product of two 6-vectors results in a bivector with 15 dimensions.
10.
Figure 6 : Energy levels of the hydrogen atom as predicted from the commutation relations of angular momentum and Laplace Runge Lenz vector operators; these energy levels have been verified experimentally.
