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arXiv:2411.08915 · European Journal of Physics

Revisiting the Laplace transform in quantum mechanics: correcting a flawed approach for the stationary Schrödinger equation

Luis M Báez, Andrés Santos

Published Jan 29, 2025• 0 citations

Abstract

Abstract 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 Eur. J. Phys. 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.

DOI: 10.1088/1361-6404/adafed

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