Since their discovery in 1927, the Heisenberg Inequalities have become an
icon of quantum mechanics. Often inappropriately referred to as the Uncertainty
Principle, these inequalities relating the standard deviations of the position
and momentum observables to Planck's constant are one of the cornerstones of
the quantum formalism even if the physical interpretation of quantum mechanics
remains still open to controversy nowadays. The Heisenberg Inequalities
governing translational motion are well understood. However, the corresponding
inequalities pertaining to rotational motion have not been established so far.
To fill this gap, we present here the Rotational Heisenberg Inequalities
relating the standard deviations of the orientation axis and orbital angular
momentum observables of an isolated molecule. The reason for choosing this
system is that a molecule separated from its environment corresponds to a bound
system preserving the orbital angular momentum.Comment: 6 pages, 2 figures. arXiv admin note: substantial text overlap with
arXiv:1412.211
