https://doi.org/10.1140/epjp/s13360-024-05741-8
Regular Article
Scaled quantum theory: the bouncing ball problem
1
Department of Physics, University of Qom, Ghadir Blvd., 371614-6611, Qom, Iran
2
Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006, Madrid, Spain
Received:
16
October
2023
Accepted:
13
October
2024
Published online:
24
October
2024
Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is described by the linear scaled von Neumann equation for mixed states and after it has been particularized to the case of pure states. The main purpose of this work is to show how this theory works for conservative systems, and the quantum-classical transition is carried out in a continuous and smooth way, being equivalent to a nonlinear differential wave equation which contains a transition parameter ranging continuously from one to zero and covering all dynamical regimes in-between the two extreme quantum and classical regimes. This parameter can be seen as a degree of quantumness where all intermediate dynamical regimes show quantum features but are fading gradually when approaching to the classical value.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.
