A differentiation formula, with application to the two-dimensional Schr\"odinger equation
Computational Physics
2026-02-03 v1 Numerical Analysis
Numerical Analysis
Quantum Physics
Abstract
A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent variable. This method is applied to the numerical solution of the eigenvalue problem for the two-dimensional Schr\"odinger equation, where standard methods converge very slowly while the approach proposed here gives accurate results.
Cite
@article{arxiv.1410.5402,
title = {A differentiation formula, with application to the two-dimensional Schr\"odinger equation},
author = {Alexander Pikovski},
journal= {arXiv preprint arXiv:1410.5402},
year = {2026}
}
Comments
3 pages