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Information and quantum theories: an analysis in one-dimensional systems

Abstract

We pedagogically present the information theory as originally established, explaining its essential ideas and paying attention to the expression employed to measure the amount of information. Also we discussed relationships between information and quantum theories. In this context we determined the information entropies on position, S_x, and momentum, S_p, spaces, besides the entropy sum S_t. Here, we use the modified entropic expressions that are dimensionally consistent. We provide original explanations for the behaviors of the S_x, S_p and S_t values analyzing the probability densities and by means of the normalization constants and properties of Fourier transform. We validate the entropic uncertainty relation and inspect the standard deviation and information entropies as measures of quantum uncertainty. The systems of interest unidimensional one-article quantum systems in ground and excited states.

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