Refinement of Uncertainty Relations in Quantum Mechanics
Quantum Physics
2025-01-30 v1
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.
Cite
@article{arxiv.2501.17165,
title = {Refinement of Uncertainty Relations in Quantum Mechanics},
author = {Sergei P. Efimov},
journal= {arXiv preprint arXiv:2501.17165},
year = {2025}
}
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6 pages