https://doi.org/10.1140/epjp/s13360-022-03466-0
Regular Article
Classical and quantum particles in the brachistochrone upper half-space
Department of Physics, Faculty of Arts and Sciences, Eastern Mediterranean University, North Cyprus via Mersin 10, Famagusta, Turkey
Received:
21
July
2022
Accepted:
5
November
2022
Published online:
13
November
2022
The brachistochrone upper half-space geometry is introduced and investigated. The classical geodesics on this curved space are found to be planar cycloids. We show that the center and radius of the cycloid depend on the initial conditions. Furthermore, we solve the Schrödinger equation for a free particle in this curved space. Due to the geometrical structure of the curved space, the free particle—free means no external nongeometric potential is applied—experiences a purely geometric potential. We utilize the point canonical transformation to bring the Schrödinger equation into its standard form where the geometric potential takes the form of a harmonic oscillator.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. 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.
