Abstract In general some operators in quantum mechanics are not commutable, which means the measurement of two or more operators can’t be done simultaneously. Angular momentum operator and Hamiltonian are examples of operators that can only be measured using a mathematical approach in the form of a commutation relationship. Based on the fifth postulate of quantum mechanics about a constant of motion, if an operator commute with Hamiltonian operator then the operator is a constant of motion. This study was conducted to examine the commutation of the angular momentum operators to the Hamiltonian operator. The commutation of the angular momentum operators <?CDATA ${\widehat{L}}_{x}$ ?> L ^ x , <?CDATA ${\widehat{L}}_{y}$ ?> L ^ y , <?CDATA ${\widehat{L}}_{z}$ ?> L ^ z , <?CDATA ${\widehat{L}}_{+}$ ?> L ^ + , and <?CDATA ${\widehat{L}}_{-}$ ?> L ^ − to the Hamiltonian operator shows that the operators are commute because the values are zero. Otherwise, the results of the component quadratic angular momentum operators commutator <?CDATA ${\widehat{L}}_{x}{}^{2}$ ?> L ^ x 2 , <?CDATA ${\widehat{L}}_{y}{}^{2}$ ?> L ^ y 2 , <?CDATA ${\widehat{L}}_{z}{}^{2}$ ?> L ^ z 2 , <?CDATA ${\widehat{L}}^{2}$ ?> L ^ 2 , <?CDATA ${L}_{+}{}^{2}$ ?> L + 2 and <?CDATA ${L}_{-}{}^{2}$ ?> LAbstract In general some operators in quantum mechanics are not commutable, which means the measurement of two or more operators can’t be done simultaneously. Angular momentum operator and Hamiltonian are examples of operators that can only be measured using a mathematical approach in the form of a commutation relationship. Based on the fifth postulate of quantum mechanics about a constant of motion, if an operator commute with Hamiltonian operator then the operator is a constant of motion. This study was conducted to examine the commutation of the angular momentum operators to the Hamiltonian operator. The commutation of the angular momentum operators <?CDATA ${\widehat{L}}_{x}$?> L ^ x , <?CDATA ${\widehat{L}}_{y}$?> L ^ y , <?CDATA ${\widehat{L}}_{z}$?> L ^ z , <?CDATA ${\widehat{L}}_{+}$?> L ^ + , and <?CDATA ${\widehat{L}}_{-}$?> L ^ − to the Hamiltonian operator shows that the operators are commute because the values are zero. Otherwise, the results of the component quadratic angular momentum operators commutator <?CDATA ${\widehat{L}}_{x}{}^{2}$?> L ^ x 2 , <?CDATA ${\widehat{L}}_{y}{}^{2}$?> L ^ y 2 , <?CDATA ${\widehat{L}}_{z}{}^{2}$?> L ^ z 2 , <?CDATA ${\widehat{L}}^{2}$?> L ^ 2 , <?CDATA ${L}_{+}{}^{2}$?> L + 2 and <?CDATA ${L}_{-}{}^{2}$?> L

Journal of Physics Conference SeriesMay 1, 20200 citations

Linear Operators and Commutators

Brian P. Anderson

SPIE eBooksSep 12, 20190 citations

Commutator Algebra

Rainer Kimmich

Springer eBooksJan 1, 19970 citations

The Bell Inequality Is Satisfied by Quantum Correlations Computed Consistently with Quantum Non-Commutation

Louis Sica

In constructing his theorem, Bell assumed that correlation functions among non-commuting variables are the same as those among commuting variables. However, in quantum mechanics, multiple data values exist simultaneously for commuting operations while for non-commuting operations data are conditional on prior outcomes, or may be predicted as alternative outcomes of the non-commuting operations. Given these qualitative differences, there is no reason why correlation functions among non-commuting variables should be the same as those among commuting variables, as assumed by Bell. When data for commuting and noncommuting operations are predicted from quantum mechanics, their correlations are different, and they now satisfy the Bell inequality.In constructing his theorem, Bell assumed that correlation functions among non-commuting variables are the same as those among commuting variables. However, in quantum mechanics, multiple data values exist simultaneously for commuting operations while for non-commuting operations data are conditional on prior outcomes, or may be predicted as alternative outcomes of the non-commuting operations. Given these qualitative differences, there is no reason why correlation functions among non-commuting variables should be the same as those among commuting variables, as assumed by Bell. When data for commuting and noncommuting operations are predicted from quantum mechanics, their correlations are different, and they now satisfy the Bell inequality.

arXiv:1507.01629Journal of Modern PhysicsJan 1, 20162 citations

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

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.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.

Journal of Physics Conference SeriesApr 1, 20193 citations

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