  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.

Quantum Physics;Atomic Physics