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

## TL;DR

This paper pedagogically explores the relationship between information theory and quantum mechanics in one-dimensional systems, analyzing entropies in position and momentum spaces and validating entropic uncertainty relations.

## Contribution

It provides a detailed analysis of information entropies in 1D quantum systems, including original explanations and validation of entropic uncertainty relations using modified, dimensionally consistent expressions.

## Key findings

- Validated entropic uncertainty relation for 1D quantum systems
- Analyzed behavior of position and momentum space entropies
- Provided original explanations for entropy behaviors in quantum states

## 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.