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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Condon–Shortley phase canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1576049 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
Target entity: Condon–Shortley phase Context triple: [Edward Condon, knownFor, Condon–Shortley phase]
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A.
Condon approximation
The Condon approximation is a simplifying assumption in molecular spectroscopy that treats electronic transition dipole moments as independent of nuclear coordinates, enabling easier calculation of vibronic transition intensities.
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B.
Longuet-Higgins
Longuet-Higgins is the surname of a notable British family that includes influential figures in theoretical chemistry, cognitive science, and mathematics.
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C.
Euler’s formula for complex exponentials
Euler’s formula for complex exponentials is the fundamental identity \(e^{i\theta} = \cos\theta + i\sin\theta\), which links complex exponentials with trigonometric functions and underpins much of complex analysis and engineering mathematics.
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D.
Huang–Rhys factor
The Huang–Rhys factor is a dimensionless parameter in solid-state and molecular spectroscopy that quantifies the strength of electron–phonon (vibronic) coupling during electronic transitions.
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E.
Huygens–Fresnel principle
The Huygens–Fresnel principle is a fundamental concept in wave optics that explains how every point on a wavefront acts as a source of secondary wavelets whose interference determines the wave’s subsequent propagation and diffraction.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Condon–Shortley phase Target entity description: The Condon–Shortley phase is a sign convention introduced in quantum mechanics to standardize the definition of spherical harmonics and angular momentum coupling coefficients.
-
A.
Condon approximation
The Condon approximation is a simplifying assumption in molecular spectroscopy that treats electronic transition dipole moments as independent of nuclear coordinates, enabling easier calculation of vibronic transition intensities.
-
B.
Longuet-Higgins
Longuet-Higgins is the surname of a notable British family that includes influential figures in theoretical chemistry, cognitive science, and mathematics.
-
C.
Euler’s formula for complex exponentials
Euler’s formula for complex exponentials is the fundamental identity \(e^{i\theta} = \cos\theta + i\sin\theta\), which links complex exponentials with trigonometric functions and underpins much of complex analysis and engineering mathematics.
-
D.
Huang–Rhys factor
The Huang–Rhys factor is a dimensionless parameter in solid-state and molecular spectroscopy that quantifies the strength of electron–phonon (vibronic) coupling during electronic transitions.
-
E.
Huygens–Fresnel principle
The Huygens–Fresnel principle is a fundamental concept in wave optics that explains how every point on a wavefront acts as a source of secondary wavelets whose interference determines the wave’s subsequent propagation and diffraction.
- F. None of above. chosen
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 |
Theory of Atomic Spectra (1935)
ⓘ
surface form:
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 Condon
ⓘ
surface form:
Edward U. Condon
G. H. Shortley ⓘ
surface form:
George 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 ⓘ |
How these facts were elicited
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Subject: Condon–Shortley phase Description of subject: The Condon–Shortley phase is a sign convention introduced in quantum mechanics to standardize the definition of spherical harmonics and angular momentum coupling coefficients.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.