Project-declaredLean 4.32.0
Angular Momentum commutation angular Momentum
QuantumMechanics.angularMomentum_commutation_angularMomentum
Project documentation
The canonical commutation relations: [xᵢ, pⱼ] = iℏ δᵢⱼ𝟙. -/ lemma position_commutation_momentum : ⁅𝐱 i, 𝐩 j⁆ = (I * ℏ) • δ[i,j] • ContinuousLinearMap.id ℂ 𝓢(Space d, ℂ) := by ext ψ x show 𝐱 i (𝐩 j ψ) x - 𝐩 j (𝐱 i ψ) x = _ trans (I * ℏ) * (-x i * ∂[j] ψ x + ∂[j] ((fun x : Space d ↦ x i) • ⇑ψ) x) · simp only [positionCLM_apply, momentumCLM_apply,...
physicsquantum field theoryrelativity
Source project: Physlib
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