Linked from

The 30 pages that link to Commutator, each with the reason it gives.

• Electric motorBroader topic: In brushed DC motors, it keeps torque directed around the rotor’s rotation.

• Quantum numberRelated: Commuting observables can have shared eigenstates and simultaneous quantum-number labels.

• Werner HeisenbergRelated: Matrix mechanics makes operator order consequential, with commutators encoding that noncommutativity.

• Lie algebraRelated: Matrix commutators are the standard source of Lie brackets.

• ObservableRelated: Commutators capture whether two observables can share definite values and compatible measurements.

• Angular momentum operatorRelated: Commutators state precisely which angular-momentum components can share eigenstates.

• Heisenberg uncertainty principleRelated: A nonzero commutator sets a lower bound on joint measurement spreads.

• Canonical commutation relationNarrower topic: The canonical relation assigns a fixed value to the position–momentum commutator.

• Conjugacy classCompared with: Commutators generate a subgroup, whereas conjugacy classes collect elements related by conjugation.

• Poisson bracketCompared with: Quantum commutators parallel Poisson brackets, with a factor of iℏ in the classical limit.

• Hamiltonian (quantum mechanics)Related: Commutators with the Hamiltonian determine time derivatives of observables in the Heisenberg picture.

• Matrix mechanicsBroader topic: Commutators encode which measured quantities can have sharply defined values together.

• Lie bracketRelated: The operator commutator is the standard model of a Lie bracket.

• Classical limitRelated: Position and momentum noncommutation weakens in appropriately scaled classical limits.

• Hamiltonian operatorNarrower topic: Commutators with the Hamiltonian determine how observables change in the Heisenberg picture.

• Pauli matricesNarrower topic: Their commutators express the noncommuting angular-momentum components.

• Solvable groupBroader topic: Commutators generate each step of the derived series.

• Jacobi identityRelated: Commutators in associative algebras provide a standard bracket satisfying the identity.

• Commutative propertyRelated: A zero commutator signals that exchanging the two factors leaves their product unchanged.

• Noncommutative algebraRelated: Commutators quantify the central feature that separates this subject from commutative algebra.

• CentralizerRelated: An element centralizes S exactly when its commutators with all members of S are identity.

• Baker–Campbell–Hausdorff formulaRelated: The first correction to the sum of exponents is their commutator.

• Pascual JordanRelated: Commutators express the algebraic relations at the heart of matrix mechanics.

• Rubik's CubeRelated: Commutators can reposition a few pieces while largely preserving others.

• Ehrenfest theoremRelated: Commutators encode the dynamical terms in the general theorem.

• Lie product formulaBroader topic: Commutators measure how far the finite products depart from commuting exponentials.

• Symmetry in quantum mechanicsBroader topic: Commutation with the Hamiltonian identifies conserved symmetry generators.

• Capelli identityNarrower topic: Commutators explain why determinants of operator entries need correction terms.

• Dixmier conjectureBroader topic: Preserving generator commutators is central to defining endomorphisms of a Weyl algebra.

• Golden–Thompson inequalityRelated: When this vanishes, the inequality becomes equality.