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arXiv · 2504.20218

Fractional Angular Momentum and Quasi-Probability Densities for Angular Degrees of Freedom

Bo-Sture K. Skagerstam·Per K. Rekdal
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Abstract

In the present update work we consider properly defined two-parameter quasi-probability densities that, e.g., can be used as witness for quantum behaviour for a class of pure states as expressed in terms of a self-adjoint observable angular position and the corresponding angular momentum operator L. It is shown that negative values of the corresponding quasi-probability densities may reveal the quantum nature of superpositions of angular momentum eigenstates with a fractional mean value of L but in an ambiguous manner. For a suitable choice of parameters these quasi-probability densities are positive and are in accordance with Borns rule in quantum mechanics. It is also shown that experimental data of the uncertainties for the angular position and L observables can be sufficient to reveal some unique quantum-mechanical features of such states without necessarily making use of quasi-probability densities.

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Bo-Sture K. Skagerstam, Per K. Rekdal. 2025-04-28. Fractional Angular Momentum and Quasi-Probability Densities for Angular Degrees of Freedom. https://arxiv.org/abs/2504.20218

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