reduced Planck constant

E26861

fundamental constant physical constant quantum 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.

Aliases (1)

reduced Planck constant ħ ×2

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 →

Referenced by (7)

Subject (surface form when different)	Predicate
Planck length ("reduced Planck constant ħ") → Planck time →	dependsOnConstant
Bekenstein bound → Bekenstein–Hawking entropy →	usesConstant
Planck constant →	hasReducedForm
Planck constant →	relatedConstant
Bekenstein bound ("reduced Planck constant ħ") →	relatesVariable