Rotational Heisenberg Inequalities

TL;DR

This paper establishes the first form of Heisenberg-like inequalities for rotational motion in molecules, relating orientation and angular momentum, filling a key gap in quantum mechanics formalism.

Contribution

It introduces the Rotational Heisenberg Inequalities, extending the fundamental uncertainty principles to rotational degrees of freedom in molecules.

Findings

Derived inequalities relating orientation and angular momentum.

Applicable to isolated, bound molecular systems.

Fills a theoretical gap in quantum mechanics formalism.

Abstract

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.