Comment on the Uncertainty Relation with Periodic Boundary Conditions

DOI10.1143/PTP.124.747zbMATH Open1205.81096arXiv1009.5820OpenAlexW3104998947MaRDI QIDQ3069457

Kazuo Fujikawa

Publication date: 26 January 2011

Published in: Progress of Theoretical Physics (Search for Journal in Brave)

Abstract: The Kennard-type uncertainty relation $DeltaxDeltap>frachbar2$ is formulated for a free particle with given momentum < hat{p}>$ inside a box with periodic boundary conditions in the large box limit. Our construction of a free particle state is analogous to that of the Bloch wave in a periodic potential. A simple Robertson-type relation, which minimizes the effect of the box boundary and may be useful in some practical applications, is also presented.

Full work available at URL: https://arxiv.org/abs/1009.5820

Mathematics Subject Classification ID

Electromagnetic interaction; quantum electrodynamics (81V10) Statistical mechanics of solids (82D20) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

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