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

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. We also discuss relationships between information and quantum theories. In this context we determine the information entropies on the position, Sx, and momentum, Sp, spaces, in addition to the entropy sum, St. Here, we use the modified entropic expressions that are dimensionally consistent. We provide original explanations for the behaviors of the Sx, Sp and St 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 are unidimensional one-particle quantum systems in the ground and excited states.