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arXiv · 2501.17165

Refinement of Uncertainty Relations in Quantum Mechanics

Sergei P. Efimov
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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.

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Sergei P. Efimov. 2025-01-03. Refinement of Uncertainty Relations in Quantum Mechanics. https://doi.org/10.1007/bf00945688

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