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Prog. Theor. Phys. Vol. 124 No. 5 (2010) pp. 747-759
Comment on the Uncertainty Relation with Periodic Boundary Conditions
Kazuo Fujikawa
Institute of Quantum Science, College of Science and Technology,
Nihon University, Tokyo 101-8308, Japan
(Received September 7, 2010)
Abstract:
The Kennard-type uncertainty relation
Δx Δp > \hbar/2
is formulated for a free particle with given momentum
<\hatp > 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.
Subject Index :
002, 013, 060
URL :
http://ptp.ipap.jp/link?PTP/124/747/
DOI : 10.1143/PTP.124.747
References:
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P. Carruthers and M. M. Nieto, Rev. Mod. Phys. 40 (1968), 411, [APS]and references therein.
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R. Jackiw, J. Math. Phys. 9 (1968), 339[CrossRef].
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K. Fujikawa, Phys. Rev. A 52 (1995), 3299[APS].
Citing Article(s) :
-
Progress of Theoretical Physics Vol. 125 No. 2 (2011) pp. 205-224
:
-
Uncertainty Relation and Probability
-
Kazuo Fujikawa and Koichiro Umetsu
