Kramers degeneracy
E415082
Kramers degeneracy is a quantum mechanical principle stating that in systems with time-reversal symmetry and half-integer spin, every energy level is at least doubly degenerate.
All labels observed (5)
| Label | Occurrences |
|---|---|
| Kramers degeneracy canonical | 4 |
| Kramers degeneracy theorem | 1 |
| Kramers doublet | 1 |
| Kramers theorem | 1 |
| Kramers theorem in quantum mechanics | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4142001 — 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: Kramers degeneracy Context triple: [Hendrik Anthony Kramers, notableWork, Kramers degeneracy]
-
A.
Russell–Saunders coupling
Russell–Saunders coupling is an atomic physics scheme that describes how individual electron orbital and spin angular momenta combine to determine the total angular momentum of an atom, especially in light atoms.
-
B.
Landau–Zener formula
The Landau–Zener formula is a quantum mechanical result that gives the probability of non-adiabatic transitions between energy levels during an avoided crossing when a system’s parameters are varied in time.
-
C.
Sommerfeld quantization rules
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.
-
D.
Jahn–Teller effect
The Jahn–Teller effect is a phenomenon in molecular and solid-state physics where electronically degenerate states cause spontaneous geometric distortions that lower a system’s symmetry and energy.
-
E.
Shubnikov–de Haas effect
The Shubnikov–de Haas effect is a quantum oscillatory phenomenon in the electrical resistance of conductors and semiconductors subjected to strong magnetic fields at low temperatures, used to probe their electronic structure and Fermi surface.
- 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: Kramers degeneracy Target entity description: Kramers degeneracy is a quantum mechanical principle stating that in systems with time-reversal symmetry and half-integer spin, every energy level is at least doubly degenerate.
-
A.
Russell–Saunders coupling
Russell–Saunders coupling is an atomic physics scheme that describes how individual electron orbital and spin angular momenta combine to determine the total angular momentum of an atom, especially in light atoms.
-
B.
Landau–Zener formula
The Landau–Zener formula is a quantum mechanical result that gives the probability of non-adiabatic transitions between energy levels during an avoided crossing when a system’s parameters are varied in time.
-
C.
Sommerfeld quantization rules
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.
-
D.
Jahn–Teller effect
The Jahn–Teller effect is a phenomenon in molecular and solid-state physics where electronically degenerate states cause spontaneous geometric distortions that lower a system’s symmetry and energy.
-
E.
Shubnikov–de Haas effect
The Shubnikov–de Haas effect is a quantum oscillatory phenomenon in the electrical resistance of conductors and semiconductors subjected to strong magnetic fields at low temperatures, used to probe their electronic structure and Fermi surface.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
physical law
ⓘ
quantum mechanical principle ⓘ |
| appliesInPresenceOf | absence of magnetic field breaking time-reversal symmetry ⓘ |
| appliesTo |
odd number of electrons in an atom or molecule with time-reversal symmetry
ⓘ
quantum systems with time-reversal symmetry ⓘ systems with half-integer total spin ⓘ |
| basedOn |
T^2 = -1 for half-integer spin
ⓘ
antiunitary nature of time-reversal operator ⓘ properties of the time-reversal operator ⓘ |
| brokenBy |
any perturbation that breaks time-reversal symmetry
ⓘ
magnetic fields ⓘ magnetic impurities ⓘ |
| category | quantum symmetry principle ⓘ |
| contrastsWith |
accidental degeneracy
ⓘ
degeneracy from spatial symmetries alone ⓘ |
| doesNotApplyTo |
systems with integer spin only
ⓘ
systems without time-reversal symmetry ⓘ |
| ensures |
at least two linearly independent states share the same energy
ⓘ
no nondegenerate eigenstates for half-integer spin with time-reversal symmetry ⓘ |
| formalizedUsing |
Wigner’s theorem on symmetry transformations
ⓘ
surface form:
Wigner’s theorem
representation theory of antiunitary symmetries ⓘ |
| hasConsequence |
pairing of states related by time-reversal
ⓘ
robustness of certain degeneracies against symmetry-preserving perturbations ⓘ |
| holdsFor |
nonrelativistic quantum systems with half-integer spin and time-reversal symmetry
ⓘ
relativistic fermions with time-reversal symmetry ⓘ |
| implies |
bands in time-reversal invariant crystals are at least doubly degenerate at time-reversal invariant momenta
ⓘ
every energy level is at least doubly degenerate ⓘ existence of degenerate pairs of states ⓘ ground state of a time-reversal invariant system with odd number of electrons is at least doubly degenerate ⓘ twofold degeneracy of energy eigenvalues ⓘ |
| mathematicallyExpressedAs | T^2 = -1 on half-integer spin states ⓘ |
| namedAfter | Hendrik Anthony Kramers ⓘ |
| relatedConcept |
Kramers degeneracy
self-linksurface differs
ⓘ
surface form:
Kramers doublet
spin-orbit coupling in solids ⓘ symmetry-protected degeneracy ⓘ time-reversal operator squaring to -1 ⓘ |
| relatesTo |
Kramers pairs
ⓘ
band structure in solids ⓘ fermionic systems ⓘ spin-1/2 particles ⓘ time-reversal symmetry in quantum mechanics ⓘ topological insulators ⓘ |
| requires |
half-integer spin
ⓘ
time-reversal symmetry ⓘ |
| usedIn |
analysis of electronic band degeneracies
ⓘ
classification of topological phases of matter ⓘ quantum transport theory ⓘ spintronics ⓘ |
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: Kramers degeneracy Description of subject: Kramers degeneracy is a quantum mechanical principle stating that in systems with time-reversal symmetry and half-integer spin, every energy level is at least doubly degenerate.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Kramers degeneracy theorem
subject surface form:
Hendrik Anthony Kramers
this entity surface form:
Kramers theorem in quantum mechanics
this entity surface form:
Kramers theorem
this entity surface form:
Kramers doublet