Comment on the uncertainty relation with periodic boundary conditions

Details Comment on the uncertainty relation with periodic boundary conditions Comment on the uncertainty relation with periodic boundary conditions

2010-09-29

arxiv.org/abs/1009.5820v1

Prog.Theor.Phys.124:747-759,2010

Physics

Quantum Physics

17 pages, to appear in Prog. Theor. Phys. (kyoto)

Scientific paper

10.1143/PTP.124.747

The Kennard-type uncertainty relation $\Delta x\Delta p >\frac{\hbar}{2}$ 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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