Refinement of Uncertainty Relations in Quantum Mechanics
arXiv:2501.17165 · doi:10.1007/BF00945688
Abstract
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg indeterminacy for two non-conjugate operators when their commutator is not a c-number. The inequality is applied to operators of the kinetic energy and coordinate of one-dimensional system. In addition, uncertainty of the angular momentum components is considered.
6 pages