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)

How this entity was disambiguated

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

Referenced by (20)

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
this entity surface form: reduced Planck constant ħ
Planck constant hasReducedForm reduced Planck constant
Planck constant relatedConstant reduced Planck constant
Planck time dependsOnConstant reduced Planck constant
Planck length dependsOnConstant reduced Planck constant
this entity surface form: reduced Planck constant ħ
matrix mechanics usesConstant reduced Planck constant
this entity surface form: Planck constant ħ
uncertainty principle constantInvolved reduced Planck constant
h-bar alsoKnownAs reduced Planck constant
subject surface form: ħ
h-bar alsoKnownAs reduced Planck constant
subject surface form: ħ
this entity surface form: Dirac constant
h-bar symbolFor reduced Planck constant
subject surface form: ħ
Planck temperature definedInTermsOf reduced Planck constant
Planck units basedOnConstant reduced Planck constant
Planck units setsToOne reduced Planck constant
this entity surface form: reduced Planck constant ħ
t_P isDerivedFrom reduced Planck constant
this entity surface form: reduced Planck constant ħ
l_P dependsOn reduced Planck constant
subject surface form: Planck length
Planck scale usesConstant reduced Planck constant
Planck area definedByConstants reduced Planck constant
this entity surface form: reduced Planck constant ħ
Planck volume definedInTermsOf reduced Planck constant
this entity surface form: reduced Planck constant ℏ