Abstract
We calculate the time-dependent Fisher information in position (F-x) and momentum (F-p) for the lowest lying state (n = 0) of two classes of
quantum damped (Lane-Emden (LE) and Caldirola-Kanai (CK)) harmonic
oscillators. The expressions of F-x and F-p are written in terms of rho,
a c-number quantity satisfying a nonlinear differential equation.
Analytical solutions of rho were obtained. For the LE and CK
oscillators, we observe that F-x increases while F-p decreases with
increasing time. The product FxFp increases and tends to a constant
value in the limit t --> infinity for the LE oscillator, while it is
time-independent for the CK oscillator. Moreover, for the CK oscillator
the product FxFp decreases as the damping (gamma) increases. Relations
among the Fisher information, Leipnik and Shannon entropies, and the
Stam and Cramer-Rao inequalities are given. A discussion on the
squeezing phenomenon in position for the oscillators is presented.
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