Heisenberg-like and Fisher-information-based uncertainty relations for $N$-electron $d$-dimensional systems

TL;DR

This paper develops generalized uncertainty relations for multi-electron systems that incorporate spatial and spin degrees of freedom, extending previous models and validating them through numerical analysis of atomic and molecular data.

Contribution

It introduces new Heisenberg-like and Fisher-information-based uncertainty relations for N-electron d-dimensional systems, accounting for spin and spatial factors.

Findings

Validated the accuracy of the new uncertainty relations numerically

Extended previous uncertainty relations to include spin and dimensionality

Applicable to atomic and molecular systems

Abstract

Heisenberg-like and Fisher-information-based uncertainty relations which extend and generalize previous similar expressions are obtained for $N$-fermion $d$-dimensional systems. The contributions of both spatial and spin degrees of freedom are taken into account. The accuracy of some of these generalized spinned uncertainty-like relations is numerically examined for a large number of atomic and molecular systems.