Condon–Shortley phase

E179791

The Condon–Shortley phase is a sign convention introduced in quantum mechanics to standardize the definition of spherical harmonics and angular momentum coupling coefficients.

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Label Occurrences
Condon–Shortley phase canonical 1

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Statements (49)

Predicate Object
instanceOf concept in quantum mechanics ⓘ
phase convention ⓘ
sign convention ⓘ
appearsIn angular momentum theory monographs ⓘ
quantum mechanics textbooks ⓘ
spectroscopic notation for atomic states ⓘ
tables of angular momentum coefficients ⓘ
appliesTo associated Legendre polynomials P_l^m(x) ⓘ
orbital angular momentum eigenstates ⓘ
spherical harmonics Y_l^m(θ,φ) ⓘ
total angular momentum eigenstates ⓘ
assumes fixed phase choice for |l,m⟩ basis ⓘ
conventionFor magnetic quantum number m dependence ⓘ
phase of Clebsch–Gordan coefficients ⓘ
phase of |l,m⟩ basis states ⓘ
defines relative sign between positive and negative m components ⓘ
sign factor (-1)^m in associated Legendre functions ⓘ
sign factor (-1)^m in spherical harmonics ⓘ
documentedIn The Theory of Atomic Spectra by Condon and Shortley ⓘ
ensures consistency between different angular momentum coupling schemes ⓘ
orthonormality of spherical harmonics with standard formulas ⓘ
simple transformation under complex conjugation of spherical harmonics ⓘ
standard parity properties of spherical harmonics ⓘ
field angular momentum theory ⓘ
atomic physics ⓘ
quantum mechanics ⓘ
hasEffect affects relative phases but not physical observables ⓘ
changes sign of some coefficients if omitted ⓘ
historicalContext introduced in early 20th century atomic spectroscopy ⓘ
motivatedBy need for consistent angular momentum algebra ⓘ
need for uniform sign conventions in spectroscopy tables ⓘ
namedAfter Edward U. Condon ⓘ
linked to: Edward Condon

George H. Shortley ⓘ
linked to: G. H. Shortley
relatedTo Clebsch–Gordan coefficients ⓘ
Wigner 3j symbols ⓘ
Wigner–Eckart theorem ⓘ
representation theory of SO(3) ⓘ
representation theory of SU(2) ⓘ
spherical tensor operators ⓘ
standardizes overall sign of angular momentum coupling coefficients ⓘ
overall sign of spherical harmonics ⓘ
relative phases of magnetic quantum number states ⓘ
usedIn angular momentum coupling coefficients ⓘ
definition of Clebsch–Gordan coefficients ⓘ
definition of Wigner 3j symbols ⓘ
definition of Wigner 6j symbols ⓘ
definition of Wigner 9j symbols ⓘ
definition of associated Legendre functions ⓘ
definition of spherical harmonics ⓘ

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Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Edward Condon → knownFor → Condon–Shortley phase ⓘ