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arXiv · 1009.5820

Comment on the uncertainty relation with periodic boundary conditions

Kazuo Fujikawa
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Abstract

The Kennard-type uncertainty relation $ΔxΔp >\frac{\hbar}{2}$ 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.

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Kazuo Fujikawa. 2010-09-29. Comment on the uncertainty relation with periodic boundary conditions. https://doi.org/10.1143/ptp.124.747

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