Angular momentum operator commutator against position and Hamiltonian of a free particle

Abstract

Observables in Quantum mechanicsare represented by operators. Its measurements cannot be determined simultaneously and the results are only a possibility. This study uses the rules of the commutator in determining the relation between angular momentum to the position and free particle Hamiltonian. The commutator will be zero if the operator that is connected can be determined simultaneously, and it will produce value if cannot be determined simultaneously. This study focused on the commutator of the angular momentum operator on the position and Hamiltonian of free particles in Cartesian coordinates. The result of the commutator of angular momentum operator to the position was zero (commut) if there wasn’t a component of the angular momentum that is equal to the position made by the commutation pair. While the results of the commutator angular momentum operator towards the free particle Hamiltonian indicated that angular momentum is the constant of motion.