https://doi.org/10.1140/epjp/s13360-024-05196-x
Regular Article
A new approach to solving the Schrödinger equation using wavefunction potentials in two and three dimensions
1
Departamento de Física, Facultad de Ciencias, Universidad de Chile, 7800003, Santiago, Chile
2
Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez, 7491169, Santiago, Chile
Received:
12
February
2024
Accepted:
18
April
2024
Published online:
7
May
2024
The Madelung–Bohm approach to Quantum Mechanics is used to extend the one-dimensional case to solve the Schrödinger equation by defining potentials for the wavefunctions in two and three dimensions. The relevance of these results to solving the phase retrieval problem (PRP) is stressed. In particular, the one-dimensional problem is solved completely and significant progress is made toward the solution of the PRP in two and three dimensions. Examples are presented.
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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.
