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arXiv · 2303.08506

Schroedinger equation on a generic radial grid

Christopher Bowen·Jean-Christophe Pain
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Abstract

In this note, we discuss the choice of radial grid in the numerical resolution of the Schroedinger equation. We detail the transformation of the equation resulting from a change of variable and function for a generic radial grid, using either the explicit or implicit form of the relation describing the change of variable, and apply it to the $a r + b \ln(r)$ log-linear mesh. It is shown that, in the former case, the first three derivatives of the Lambert $W$ function are required. This complication becomes unnecessary if we adopt the implicit relation instead.

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Christopher Bowen, Jean-Christophe Pain. 2023-03-15. Schroedinger equation on a generic radial grid. https://doi.org/10.1016/j.hedp.2023.101042

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