Uncertainty for spin systems
Abstract
A modified definition of quantum mechanical uncertainty D for spin systems, which is invariant under the action of SU(2), is suggested. Its range is shown to be h2j<D<h2j(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(D)=h2j(j+1/2). The most used sets of coherent states in spin systems coincide with the set of minimum D uncertainty states.
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