L_i operators satisfy [L_i, L_j] = iℏ ε_{ijk} L_k; eigenvalues L² = ℏ²ℓ(ℓ+1), L_z = ℏm with ℓ ∈ {0, ½, 1, …} and m ∈ {−ℓ, …, ℓ}.
Quantum angular momentum
Related concepts
- Canonical commutation relation
- Quantum spin
- Wigner's classification of particles
- Every natural number has a successor
- SU(2) CG: (½)⊗(½) = 1 ⊕ 0
- Pauli algebra: tr(σ_iσ_j) = 2δ_{ij}, [σ_i,σ_j] = 2iε_{ijk}σ_k
- Period length 2n^2 rule from Pauli-exclusion shell filling (periodic-table)
- Hueckel pi-MO eigenvalues of benzene: epsilon_k = alpha + 2 beta cos(2 pi k / 6) (molecules)