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.

arXiv commentVersion accepted for publication in European Journal of Physics

References in corpus (8)

• Entropic Uncertainty Relations and their Applications
• Universal Uncertainty Relations
• Shannon Information Entropy in Heavy-ion Collisions
• Shannon entropy: a study of confined hydrogenic-like atoms
• Contradictory uncertainty relations
• Entropic uncertainty measures for large dimensional hydrogenic systems
• The different paths to entropy
• Quantum information measures of the one-dimensional Robin quantum well

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• Informational analysis of the confinement of an electron in an asymmetric double quantum dot
• Evaluating Bohm's quantum force in the scattering process by a classical potential