Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra
E463101
"Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra" is a foundational monograph by Eugene Wigner that systematically applies group-theoretical methods to analyze the symmetries and energy levels of atomic systems in quantum mechanics.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra canonical | 1 |
| The Theory of Groups and Quantum Mechanics | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4721229 — 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.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra Context triple: [Wigner Jenő Pál, notableWork, Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra]
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A.
Gruppentheorie und Quantenmechanik
Gruppentheorie und Quantenmechanik is Hermann Weyl’s influential 1928 monograph that systematically applies group theory to the foundations of quantum mechanics, shaping the mathematical formulation of modern physics.
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B.
Theory of Atomic Spectra (1935)
Theory of Atomic Spectra (1935) is a foundational physics monograph by Edward Condon that systematically develops the quantum-mechanical theory underlying atomic spectral lines and their structure.
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C.
Wigner–Eckart theorem
The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
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D.
Herzberg trilogy on molecular spectra
The Herzberg trilogy on molecular spectra is a foundational multi-volume work that systematically presents the theory and experimental data of molecular spectroscopy, authored by Nobel laureate Gerhard Herzberg.
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E.
Theory of Groups
Theory of Groups is a foundational textbook in abstract algebra that systematically develops the theory of groups and has been widely used for advanced mathematical study and research.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra Target entity description: "Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra" is a foundational monograph by Eugene Wigner that systematically applies group-theoretical methods to analyze the symmetries and energy levels of atomic systems in quantum mechanics.
-
A.
Gruppentheorie und Quantenmechanik
Gruppentheorie und Quantenmechanik is Hermann Weyl’s influential 1928 monograph that systematically applies group theory to the foundations of quantum mechanics, shaping the mathematical formulation of modern physics.
-
B.
Theory of Atomic Spectra (1935)
Theory of Atomic Spectra (1935) is a foundational physics monograph by Edward Condon that systematically develops the quantum-mechanical theory underlying atomic spectral lines and their structure.
-
C.
Wigner–Eckart theorem
The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
-
D.
Herzberg trilogy on molecular spectra
The Herzberg trilogy on molecular spectra is a foundational multi-volume work that systematically presents the theory and experimental data of molecular spectroscopy, authored by Nobel laureate Gerhard Herzberg.
-
E.
Theory of Groups
Theory of Groups is a foundational textbook in abstract algebra that systematically develops the theory of groups and has been widely used for advanced mathematical study and research.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
physics textbook ⓘ scientific monograph ⓘ |
| associatedWith | Eugene Wigner's work on symmetry principles ⓘ |
| author | Eugene Wigner NERFINISHED ⓘ |
| contribution |
clarified role of symmetry in degeneracy of atomic energy levels
ⓘ
introduced systematic use of group theory in atomic spectroscopy ⓘ provided group-theoretical derivation of selection rules ⓘ |
| field |
atomic physics
ⓘ
group theory ⓘ quantum mechanics ⓘ |
| focus |
application of mathematical group theory to physical spectra
ⓘ
connection between symmetry groups and observable spectral patterns ⓘ |
| historicalPeriod | 20th-century theoretical physics ⓘ |
| influenced |
development of modern quantum theory textbooks
ⓘ
use of group theory in atomic and molecular physics ⓘ |
| language | English ⓘ |
| notableFor | early comprehensive treatment of group theory in quantum mechanics ⓘ |
| topic |
Clebsch–Gordan coefficients
NERFINISHED
ⓘ
Lie algebras NERFINISHED ⓘ Lie groups ⓘ Wigner–Eckart theorem NERFINISHED ⓘ addition of angular momenta ⓘ angular momentum in quantum mechanics ⓘ atomic spectra ⓘ degeneracy of energy levels ⓘ energy levels of atoms ⓘ fine structure of atomic spectra ⓘ hyperfine structure ⓘ identical particles in quantum mechanics ⓘ irreducible representations ⓘ permutation symmetry ⓘ point groups ⓘ representation theory ⓘ rotation group ⓘ selection rules ⓘ space quantization ⓘ spectral line intensities ⓘ spectroscopic notation ⓘ symmetry in quantum mechanics ⓘ symmetry operations ⓘ tensor operators ⓘ term symbols of atomic states ⓘ |
| usedIn |
advanced courses on quantum mechanics
ⓘ
courses on group theory in physics ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra Description of subject: "Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra" is a foundational monograph by Eugene Wigner that systematically applies group-theoretical methods to analyze the symmetries and energy levels of atomic systems in quantum mechanics.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
Wigner Jenő Pál
→
notableWork
→
Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra
ⓘ
Gruppentheorie und Quantenmechanik
→
relatedWork
→
Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra
ⓘ
this entity surface form:
The Theory of Groups and Quantum Mechanics