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| Format: | Preprint |
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2024
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| Online-Zugang: | https://arxiv.org/abs/2411.08915 |
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| _version_ | 1866929725568450560 |
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| author | Báez, Luis M. Santos, Andrés |
| author_facet | Báez, Luis M. Santos, Andrés |
| contents | The Laplace transform is a valuable tool in physics, particularly in solving differential equations with initial or boundary conditions. A 2014 study by Tsaur and Wang (2014 \emph{Eur.~J.~Phys.} \textbf{35} 015006) introduced a Laplace-transform-based method to solve the stationary Schrödinger equation for various potentials. However, their approach contains critical methodological flaws: the authors disregard essential boundary conditions and apply the residue theorem incorrectly in the inverse transformation process. These errors ultimately cancel out, leading to correct results despite a flawed derivation. In this paper, we revisit the use of the Laplace transform for the one-dimensional Schrödinger equation, clarifying correct practices in handling boundary conditions and singularities. This analysis offers a sound and consistent framework for the application of Laplace transforms in stationary quantum mechanics, underscoring their educational utility in quantum mechanics coursework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08915 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting the Laplace transform in quantum mechanics: correcting a flawed approach for the stationary Schrödinger equation Báez, Luis M. Santos, Andrés Quantum Physics Physics Education The Laplace transform is a valuable tool in physics, particularly in solving differential equations with initial or boundary conditions. A 2014 study by Tsaur and Wang (2014 \emph{Eur.~J.~Phys.} \textbf{35} 015006) introduced a Laplace-transform-based method to solve the stationary Schrödinger equation for various potentials. However, their approach contains critical methodological flaws: the authors disregard essential boundary conditions and apply the residue theorem incorrectly in the inverse transformation process. These errors ultimately cancel out, leading to correct results despite a flawed derivation. In this paper, we revisit the use of the Laplace transform for the one-dimensional Schrödinger equation, clarifying correct practices in handling boundary conditions and singularities. This analysis offers a sound and consistent framework for the application of Laplace transforms in stationary quantum mechanics, underscoring their educational utility in quantum mechanics coursework. |
| title | Revisiting the Laplace transform in quantum mechanics: correcting a flawed approach for the stationary Schrödinger equation |
| topic | Quantum Physics Physics Education |
| url | https://arxiv.org/abs/2411.08915 |