To what extent do position and momentum commute?

José Francisco García Juliá

Nicolae Cotfas

Bambang Supriadi, Trapsilo Prihandono, V Rizqiyah +3 more

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.

John Price

Qi-Jun Yin, Jian-zu Zhang A B

In two-dimensional space a subtle point that for the case of both space–space and momentum–momentum non-commuting, different from the case of only space–space non-commuting, the deformed Heisenberg–Weyl algebra in non-commutative space is not completely equivalent to the undeformed Heisenberg–Weyl algebra in commutative space is clarified. It follows that there is no well-defined procedure to construct the deformed position–position coherent state or the deformed momentum–momentum coherent state from the undeformed position–momentum coherent state. Identifications of the deformed position–position and deformed momentum–momentum coherent states with the lowest energy states of a cold Rydberg atom in special conditions and a free particle, respectively, are demonstrated.

lVL Mzla I

An investigation is made of the extent to which harmonicoscillator coherent states can bc used to describe superconductivity and Joscphson tunneling phenomena. Recent work has utilized angularmomentum commutation relations for operators that create and annihilate pairs in a Josephson device. This formalism utilizes certain approximations in obtaining angular-momentum commutation rules for the superconducting tunnel junction. We apply the coupled harmonicoscillator approach due to Schwinger to regain angular-momentum commutation relations.