Abstract
We analyze the noncommutativity effects on the Fisher information (F-(r)
over cap,((p) over cap)) and Shannon entropies (S-(r) over cap,((p) over
cap)) of a harmonic oscillator immersed in a time-varying electric field
in two and three dimensions. We find the exact solutions of the
respective time-dependent Schrodinger equation and use them to calculate
the Fisher information and the Shannon entropy for the simplest case
corresponding to the lowest-lying state of each system. While there is
no problem in defining the Shannon entropy for noncommutating spaces,
the definition of the Fisher information have to be modified to satisfy
the Cramer-Rao inequalities. For both systems we observe how the Fisher
information and Shannon entropy in position and momentum change due to
the noncommutativity of the space. We verify that the
Bialynicki-Birula-Mycielski (BBM) entropic uncertainty relation still
holds in the systems considered. (C) 2017 Elsevier B.V. All rights
reserved.
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