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arXiv · 1612.06706

The Coulomb potential in quantum mechanics revisited

A. A. Othman·M. de Montigny·F. Marsiglio
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Abstract

The procedure commonly used in textbooks for determining the eigenvalues and eigenstates for a particle in an attractive Coulomb potential is not symmetric in the way the boundary conditions at $r=0$ and $r \rightarrow \infty$ are considered. We highlight this fact by solving a model for the Coulomb potential with a cutoff (representing the finite extent of the nucleus); in the limit that the cutoff is reduced to zero we recover the standard result, albeit in a non-standard way. This example is used to emphasize that a more consistent approach to solving the Coulomb problem in quantum mechanics requires an examination of the non-standard solution. The end result is, of course, the same.

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A. A. Othman, M. de Montigny, F. Marsiglio. 2016-12-16. The Coulomb potential in quantum mechanics revisited. https://doi.org/10.1119/1.4976829

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