Heisenberg uncertainty relation and statistical measures in the square well

TL;DR

This paper investigates the relationship between the Heisenberg uncertainty principle and statistical measures like complexity and entropy in a quantum particle confined in a square well, revealing coinciding extremal values.

Contribution

It introduces a comparative analysis of quantum uncertainty and statistical measures in a non-stationary square well system, highlighting their temporal correlations.

Findings

Extreme values of xp coincide with those of statistical measures.

Statistical complexity and Fisher-Shannon entropy vary with time in the system.

Heisenberg uncertainty relation aligns with statistical measures at extremal points.

Abstract

A non stationary state in the one-dimensional infinite square well formed by a combination of the ground state and the first excited one is considered. The statistical complexity and the Fisher-Shannon entropy in position and momentum are calculated with time for this system. These measures are compared with the Heisenberg uncertainty relation, \Delta x\Delta p. It is observed that the extreme values of \Delta x\Delta p coincide in time with extreme values of the other two statistical magnitudes.