Modified information entropies in one-dimensional quantum systems
Wallas S. Nascimento, Marina de Godoy Almeida, Frederico V. Prudente · arXiv (Cornell University) · 2019
The present research offers a connection between information and quantum theories considering, as a bridge, the informational entropy. The information theory is explored as originally developed and links with the quantum theory are investigated. In this context are presented the information entropies on position, $S_r$, and momentum, $S_p$, spaces. The entropy sum $S_t$ is defined by adding $S_r$ and $S_p$ entropies. From $S_t$ entropy, we obtain uncertainty relation. We study the behavior of modified entropic expressions (dimensionally adequate), to inspect the phenomena of localization or delocalization of the probability densities through of the information entropies and make an energy analysis. The systems of interest are one-dimensional quantum systems (particle in a box and harmonic oscillator) in ground and excited states.