Fractional Angular Momentum and Quasi-Probability Densities for Angular Degrees of Freedom
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914506849910784 |
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| author | Skagerstam, Bo-Sture K. Rekdal, Per K. |
| author_facet | Skagerstam, Bo-Sture K. Rekdal, Per K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20218 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Angular Momentum and Quasi-Probability Densities for Angular Degrees of Freedom Skagerstam, Bo-Sture K. Rekdal, Per K. Quantum Physics Mathematical Physics 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. |
| title | Fractional Angular Momentum and Quasi-Probability Densities for Angular Degrees of Freedom |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2504.20218 |