Sommerfeld quantization rules
E234760
Sommerfeld quantization rules are an early quantum theory refinement of Bohr’s model that quantize electron motion in elliptical orbits using action integrals, helping to explain fine-structure details in atomic spectra.
All labels observed (9)
How this entity was disambiguated
This entity first appeared as the object of triple T2093718 — 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: Sommerfeld quantization rules Context triple: [Arnold Sommerfeld, knownFor, Sommerfeld quantization rules]
-
A.
Vorlesungen über Atommechanik
Vorlesungen über Atommechanik is a foundational early 20th-century textbook on quantum theory and atomic mechanics written by physicist Max Born.
-
B.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
-
C.
Quantum Mechanics (with Philip M. Morse)
"Quantum Mechanics (with Philip M. Morse)" is a foundational early 20th-century textbook on quantum theory co-authored by physicists Edward Condon and Philip M. Morse.
-
D.
The Principles of Quantum Mechanics
The Principles of Quantum Mechanics is a foundational 1930 textbook by Paul Dirac that rigorously formalized quantum theory and introduced key concepts such as bra–ket notation.
-
E.
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.
- 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: Sommerfeld quantization rules Target entity description: Sommerfeld quantization rules are an early quantum theory refinement of Bohr’s model that quantize electron motion in elliptical orbits using action integrals, helping to explain fine-structure details in atomic spectra.
-
A.
Vorlesungen über Atommechanik
Vorlesungen über Atommechanik is a foundational early 20th-century textbook on quantum theory and atomic mechanics written by physicist Max Born.
-
B.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
-
C.
Quantum Mechanics (with Philip M. Morse)
"Quantum Mechanics (with Philip M. Morse)" is a foundational early 20th-century textbook on quantum theory co-authored by physicists Edward Condon and Philip M. Morse.
-
D.
The Principles of Quantum Mechanics
The Principles of Quantum Mechanics is a foundational 1930 textbook by Paul Dirac that rigorously formalized quantum theory and introduced key concepts such as bra–ket notation.
-
E.
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.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
old quantum theory
ⓘ
physical theory ⓘ quantization rule ⓘ |
| aimsTo | quantize multi-dimensional periodic motion ⓘ |
| alternativeName |
Sommerfeld quantization rules
ⓘ
surface form:
Bohr–Sommerfeld quantization rules
|
| appliesTo |
bound systems
ⓘ
electron orbits ⓘ elliptical orbits ⓘ integrable Hamiltonian systems ⓘ |
| assumes |
classical trajectories
ⓘ
elliptical Kepler orbits for electrons ⓘ |
| basedOn | action integral quantization ⓘ |
| compatibleWith |
Sommerfeld quantization rules
self-linksurface differs
ⓘ
surface form:
Bohr–Sommerfeld quantization
|
| explains | relativistic corrections to hydrogen energy levels (partially) ⓘ |
| extends |
Sommerfeld quantization rules
self-linksurface differs
ⓘ
surface form:
Bohr quantization condition
|
| field |
atomic physics
ⓘ
quantum physics ⓘ theoretical physics ⓘ |
| formulatedBy | Arnold Sommerfeld ⓘ |
| helpsExplain |
Zeeman effect
ⓘ
anomalies in hydrogen spectral lines ⓘ fine-structure splitting in atomic spectra ⓘ |
| historicalContext | old quantum theory between classical mechanics and modern quantum mechanics ⓘ |
| historicalPeriod | early 20th century ⓘ |
| influenced | development of quantum mechanics ⓘ |
| involves |
action-angle variables
ⓘ
closed phase-space trajectories ⓘ |
| mathematicalDomain |
Hamiltonian mechanics
ⓘ
canonical transformations ⓘ |
| motivatedBy | fine structure of hydrogen spectrum ⓘ |
| namedAfter | Arnold Sommerfeld ⓘ |
| precedes |
matrix mechanics
ⓘ
wave mechanics ⓘ |
| quantizes | action integrals over closed paths ⓘ |
| refines |
Bohr model of the atom
ⓘ
surface form:
Bohr model
|
| relatedTo |
EBK quantization
ⓘ
Sommerfeld fine-structure formula ⓘ WKB approximation ⓘ |
| status | historically important but superseded ⓘ |
| typeOf | semi-classical quantization ⓘ |
| usesConcept |
action variable
ⓘ
adiabatic invariant ⓘ azimuthal quantum number ⓘ principal quantum number ⓘ radial quantum number ⓘ |
| usesMathematicalForm | ∮ p_i dq_i = n_i h ⓘ |
| yearProposed | 1916 ⓘ |
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: Sommerfeld quantization rules Description of subject: Sommerfeld quantization rules are an early quantum theory refinement of Bohr’s model that quantize electron motion in elliptical orbits using action integrals, helping to explain fine-structure details in atomic spectra.
Referenced by (10)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Sommerfeld–Wilson quantization
this entity surface form:
old quantum theory
this entity surface form:
Sommerfeld model of the atom
this entity surface form:
Old Quantum Theory
this entity surface form:
Bohr–Sommerfeld quantization
this entity surface form:
Bohr quantization condition
Sommerfeld quantization rules
→
compatibleWith
→
Sommerfeld quantization rules
self-linksurface differs
ⓘ
this entity surface form:
Bohr–Sommerfeld quantization
this entity surface form:
Bohr–Sommerfeld quantization rules
this entity surface form:
Bohr–Sommerfeld model