Pauli effects in uncertainty relations

TL;DR

This paper investigates how the spin dimensionality of fermionic systems influences two forms of the uncertainty principle, analyzing atomic data from Hydrogen to Lawrencium to assess the accuracy of these modified relations.

Contribution

It introduces spin-dependent modifications to the uncertainty relations and evaluates their accuracy across a range of atoms within a self-consistent framework.

Findings

Spin effects significantly alter uncertainty bounds.

Modified relations show improved accuracy for heavier atoms.

Results validate the importance of spin considerations in quantum uncertainty.

Abstract

In this letter we analyze the effect of the spin dimensionality of a physical system in two mathematical formulations of the uncertainty principle: a generalized Heisenberg uncertainty relation valid for all antisymmetric N-fermion wavefunctions, and the Fisher-information- based uncertainty relation valid for all antisymmetric N-fermion wavefunctions of central potentials. The accuracy of these spin-modified uncertainty relations is examined for all atoms from Hydrogen to Lawrencium in a self-consistent framework.