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.
Facts
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 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Wigner-Eckart theorem, Wikipedia
Sources
1. Wigner-Eckart theorem, Wikipedia
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.
- In Branch: Representation Theory, Lead sentence
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.