The Wigner-Eckart Theorem is a result of representation theory and quantum mechanics stating that the matrix elements of a spherical tensor operator, computed in the basis of angular momentum eigenstates, can always be written as the product of two factors: one independent of the states' orientation in space, and a Clebsch-Gordan coefficient that carries all of the orientation dependence. Named for Eugene Wigner and Carl Eckart, it links the symmetry transformation groups of space to the conservation of angular momentum.
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StatementThe matrix elements of a spherical tensor operator, taken in the basis of angular momentum eigenstates, can be written as the product of two factors, one independent of orientation and the other a Clebsch-Gordan coefficient that carries the orientation dependence. 1 Classification
Statement Form Wigner-Eckart Theorem
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Source Wigner-Eckart theorem, Wikipedia
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Introduction
It states that matrix elements of spherical tensor operators in the basis of angular momentum eigenstates can be expressed as the product of two factors, one of which is independent of angular momentum orientation, and the other a Clebsch-Gordan coefficient.
Proved By: Eugene Wigner, Lead sentence
The name derives from physicists Eugene Wigner and Carl Eckart, who developed the formalism as a link between the symmetry transformation groups of space (applied to the Schrödinger equations) and the principles of conservation of energy, momentum, and angular momentum.
Principal Result Of: Eugene Wigner, Lead sentence of the article on the result
The name derives from physicists Eugene Wigner and Carl Eckart, who developed the formalism as a link between the symmetry transformation groups of space (applied to the Schrödinger equations) and the principles of conservation of energy, momentum, and angular momentum.
- In Branch: Representation Theory, Lead sentence
In Group: Quantum Mechanics and Quantum Field Theory, Lead section
theorem is a theorem of representation theory and quantum mechanics. It states that matrix elements of spherical
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