https://doi.org/10.1140/epjp/s13360-025-07091-5
Regular Article
Quantum Newtonian cosmology revisited in Wigner–Weyl transforms: a phase space perspective
1
PTEA Laboratory, Physics department, Faculty of sciences, Yahia FARES University, 26000, Médéa, Algeria
2
LPTHIRM, Département de physique, Faculté des sciences, Université Saâd DAHLAB-Blida 1, B.P. 270 Route de Soumâa, 09000, Blida, Algeria
a
cherroud.othmane@univ-medea.dz
Received:
15
September
2025
Accepted:
18
November
2025
Published online:
28
November
2025
The affine quantization of a Hamiltonian operator in quantum Newtonian cosmology allows us to find exact solutions to the Schrödinger equation. In parallel, we developed an alternative approach to Newtonian quantum mechanics in phase space, enabling us to derive analytical expressions for Wigner’s distribution functions of moments associated with position and momentum operators of higher orders. Our study also explores the properties of the position operator and the general formula for the oscillation frequency for each state in the quantum Newtonian cosmology. Furthermore, we verify the Dirac commutation relation and the generality of Heisenberg’s uncertainty principle.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
