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.

AI illustration

How this image was made

AI-generated illustration of reduced Planck constant

This AI-generated illustration was produced by black-forest-labs/FLUX.2-dev (1024x1024) from a prompt written by openai/gpt-oss-120b from the entity's label + description.

Prompt

Generate an image of a reduced Planck constant (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 (6)

How this entity was disambiguated

Statements (49)

Predicate Object
instanceOf fundamental constant ⓘ
physical constant ⓘ
quantum constant ⓘ
alsoKnownAs h-bar ⓘ
ħ ⓘ
appearsIn Bohr model ⓘ
Dirac equation ⓘ
Feynman rules ⓘ
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

Referenced by (26)

Full triples — surface form annotated when it differs from this entity's canonical label.

Bekenstein–Hawking entropy → usesConstant → reduced Planck constant ⓘ
Bekenstein bound → usesConstant → reduced Planck constant ⓘ
Bekenstein bound → relatesVariable → reduced Planck constant ħ ⓘ
linked to: reduced Planck constant
Planck constant → hasReducedForm → reduced Planck constant ⓘ
Planck constant → relatedConstant → reduced Planck constant ⓘ
Planck time → dependsOnConstant → reduced Planck constant ⓘ
Planck length → dependsOnConstant → reduced Planck constant ħ ⓘ
linked to: reduced Planck constant
matrix mechanics → usesConstant → Planck constant ħ ⓘ
linked to: reduced Planck constant
uncertainty principle → constantInvolved → reduced Planck constant ⓘ
ħ → alsoKnownAs → reduced Planck constant ⓘ
subject linked to: h-bar
ħ → alsoKnownAs → Dirac constant ⓘ
subject linked to: h-bar
linked to: reduced Planck constant
ħ → symbolFor → reduced Planck constant ⓘ
subject linked to: h-bar
Planck temperature → definedInTermsOf → reduced Planck constant ⓘ
Planck units → basedOnConstant → reduced Planck constant ⓘ
Planck units → setsToOne → reduced Planck constant ħ ⓘ
linked to: reduced Planck constant
t_P → isDerivedFrom → reduced Planck constant ħ ⓘ
linked to: reduced Planck constant
Planck length → dependsOn → reduced Planck constant ⓘ
subject linked to: l_P
Planck scale → usesConstant → reduced Planck constant ⓘ
Planck area → definedByConstants → reduced Planck constant ħ ⓘ
linked to: reduced Planck constant
Planck volume → definedInTermsOf → reduced Planck constant ℏ ⓘ
linked to: reduced Planck constant
Mott minimum metallic conductivity → dependsOn → reduced Planck constant ħ ⓘ
linked to: reduced Planck constant
Moyal product → parameter → Planck constant ℏ ⓘ
linked to: reduced Planck constant
Dirac quantization condition → relatesQuantity → Planck constant ħ ⓘ
linked to: reduced Planck constant
Planck density → isDerivedFromConstant → reduced Planck constant ⓘ
Planck power → definedInTermsOf → reduced Planck constant ⓘ
EBK quantization → usesQuantity → Planck constant ħ ⓘ
linked to: reduced Planck constant