Uncertainty for spin systems

A modified definition of quantum mechanical uncertainty Δ for spin systems, which is invariant under the action of SU(2), is suggested. Its range is shown to be ℏ2j⩽Δ⩽ℏ2j(j+1) within any irreducible representation j of SU(2) and its mean value in Hilbert space computed using the Fubini–Study metric is determined to be mean(Δ)=ℏ2j(j+1/2). The most used sets of coherent states in spin systems coincide with the set of minimum Δ uncertainty states.