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arXiv:1405.6478 · Acta Physica Polonica A

Semiclassical Double-Inequality on Heisenberg Uncertainty Relation in 1D

Klaus Bering

Published Jun 1, 2016• 0 citations
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Abstract

We prove a double-inequality for the product of uncertainties for position and momentum of bound states for 1D quantum mechanical systems in the semiclassical limit.
DOI
10.12693/aphyspola.129.1093

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Since the publication of Heisenberg’s paper1 on the “anschaulichen Inhalt” of quantum mechanics, discussions of the fundamental limitations on the accuracy of physical measurements have been much in the foreground. According to Heisenberg, the quantum mechanics implies that it is impossible to measure simultaneous values of a coordinate and its conjugate momentum with unlimited precision. Instead, if Δp be the estimated error or uncertainty in a momentum and Δq that in the associated coordinate one must have the inequality, ΔpΔq>h2π \Delta p\Delta q>\frac{h}{{2\pi}} ΔpΔq>2πh​ (1) This inequality has come to be known quite generally as Heisenberg’s uncertainty relation.