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A new approach to solving the Schrödinger equation using wavefunction potentials in two and three dimensions

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Abstract

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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Authors and Affiliations

  1. Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, 7800003, Chile

    Valentina A. Villaflor, V. Alejandro Muñoz-Mosqueira & Sergio A. Hojman

  2. Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez, Santiago, 7491169, Chile

    Sergio A. Hojman

Authors
  1. Valentina A. Villaflor
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  2. V. Alejandro Muñoz-Mosqueira
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  3. Sergio A. Hojman
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Correspondence to Sergio A. Hojman.

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Villaflor, V.A., Muñoz-Mosqueira, V.A. & Hojman, S.A. A new approach to solving the Schrödinger equation using wavefunction potentials in two and three dimensions. Eur. Phys. J. Plus 139, 391 (2024). https://doi.org/10.1140/epjp/s13360-024-05196-x

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