reduced Planck constant
E26861
The reduced Planck constant (ħ) is a fundamental physical constant that quantifies the scale of quantum effects, commonly appearing in formulations of quantum mechanics and quantum field theory.
All labels observed (5)
| Label | Occurrences |
|---|---|
| reduced Planck constant canonical | 12 |
| reduced Planck constant ħ | 5 |
| Dirac constant | 1 |
| Planck constant ħ | 1 |
| reduced Planck constant ℏ | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T210595 — 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: reduced Planck constant Context triple: [Bekenstein–Hawking entropy, usesConstant, reduced Planck constant]
-
A.
Boltzmann constant
The Boltzmann constant is a fundamental physical constant that links temperature to energy at the particle level, playing a central role in statistical mechanics and thermodynamics.
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B.
Newtonian gravitational constant G
The Newtonian gravitational constant G is the fundamental physical constant that quantifies the strength of gravitational attraction between masses in classical and relativistic theories of gravity.
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C.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
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D.
Dirac equation
The Dirac equation is a fundamental relativistic wave equation in quantum mechanics that describes spin-½ particles such as electrons and predicts phenomena like antimatter.
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E.
Schwarzschild radius
The Schwarzschild radius is the critical distance from the center of a non-rotating, spherically symmetric mass at which its escape velocity equals the speed of light, defining the boundary of a black hole.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: reduced Planck constant Target entity description: The reduced Planck constant (ħ) is a fundamental physical constant that quantifies the scale of quantum effects, commonly appearing in formulations of quantum mechanics and quantum field theory.
-
A.
Boltzmann constant
The Boltzmann constant is a fundamental physical constant that links temperature to energy at the particle level, playing a central role in statistical mechanics and thermodynamics.
-
B.
Newtonian gravitational constant G
The Newtonian gravitational constant G is the fundamental physical constant that quantifies the strength of gravitational attraction between masses in classical and relativistic theories of gravity.
-
C.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
D.
Dirac equation
The Dirac equation is a fundamental relativistic wave equation in quantum mechanics that describes spin-½ particles such as electrons and predicts phenomena like antimatter.
-
E.
Schwarzschild radius
The Schwarzschild radius is the critical distance from the center of a non-rotating, spherically symmetric mass at which its escape velocity equals the speed of light, defining the boundary of a black hole.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
fundamental constant
ⓘ
physical constant ⓘ quantum constant ⓘ |
| alsoKnownAs |
h-bar
ⓘ
ħ ⓘ |
| appearsIn |
Bohr model of the atom
ⓘ
surface form:
Bohr model
Dirac equation ⓘ Feynman rules ⓘ uncertainty principle ⓘ
surface form:
Heisenberg uncertainty principle
Klein–Gordon equation ⓘ Schrödinger equation ⓘ angular momentum operator ⓘ canonical quantization ⓘ commutation relations ⓘ path integral formulation ⓘ quantum field theory ⓘ quantum mechanics ⓘ spin operator ⓘ |
| CODATA2022Uncertainty | exact (defined via h) ⓘ |
| CODATA2022Value | 1.054571817e-34 J·s ⓘ |
| definedAs | Planck constant divided by 2π ⓘ |
| dimension |
action
ⓘ
angular momentum ⓘ |
| entersEquation |
L̂ = -iħ r × ∇
ⓘ
Ŝ = ħ σ/2 ⓘ [x̂, p̂] = iħ ⓘ iħ ∂ψ/∂t = Ĥψ ⓘ Δx Δp ≥ ħ/2 ⓘ |
| exactValueReason | Planck constant is fixed in SI ⓘ |
| field |
condensed matter physics
ⓘ
particle physics ⓘ theoretical physics ⓘ |
| isPartOf |
Planck units system
ⓘ
natural units system ⓘ |
| mathematicalDefinition | ħ = h / (2π) ⓘ |
| naturalUnitsValue | 1 (in many natural unit systems) ⓘ |
| relatedConstant | Planck constant ⓘ |
| relatedQuantity |
Bohr magneton
ⓘ
fine-structure constant ⓘ quantum of action ⓘ |
| role |
relates energy and frequency via Planck constant
ⓘ
sets the scale of quantum effects ⓘ |
| SIUnit | joule second ⓘ |
| SIUnitSymbol | J·s ⓘ |
| symbol | ħ ⓘ |
| usedFor |
defining Planck units
ⓘ
defining natural units ⓘ expressing commutators of operators ⓘ expressing uncertainty relations ⓘ |
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.
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.
Subject: reduced Planck constant Description of subject: The reduced Planck constant (ħ) is a fundamental physical constant that quantifies the scale of quantum effects, commonly appearing in formulations of quantum mechanics and quantum field theory.
Referenced by (20)
Full triples — surface form annotated when it differs from this entity's canonical label.