https://doi.org/10.1140/epjp/s13360-025-05969-y
Regular Article
A possible solution to Einstein’s problem of 1953: the velocity of a quantum particle in a box
1
Department of Engineering, University of Sannio, Piazza Roma 21, 82100, Benevento, BN, Italy
2
Department of Computer Science, University of Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy
3
, Lindau, Bodensee, Germany
Received:
29
October
2024
Accepted:
31
December
2024
Published online:
14
January
2025
According to the prediction of the classical physics, a macroscopic body moves oscillating between two perfectly reflecting walls with a velocity proportional to its energy. On the contrary, the momentum of the body calculated in the framework of the de Broglie–Bohm interpretation of quantum mechanics is vanishing. This result was considered unsatisfactory by Einstein and other scientists who believed that also for quantum particles, it must be possible to move in an oscillatory way. In order to give an answer to Einstein’s objection, we show that it is possible to obtain a motion of the body using the standard rules of quantum mechanics. We obtain a correction of the Schrödinger equation, and we calculate explicitly the solution for the case of the particle in a box. Finally, we find the expression of the quantum velocity.
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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.
