Comment on the Uncertainty Relation with Periodic Boundary Conditions
K. Fujikawa · Progress of Theoretical Physics · 2010
The Kennard-type uncertainty relation is formulated for a free particle with given momentum 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.