# Efficient Spectral and Spectral Element Methods for Eigenvalue Problems of Schrödinger Equations with an Inverse Square Potential

@article{Li2016EfficientSA,
title={Efficient Spectral and Spectral Element Methods for Eigenvalue Problems of Schr{\"o}dinger Equations with an Inverse Square Potential},
author={Huiyuan Li and Zhimin Zhang},
journal={SIAM J. Scientific Computing},
year={2016},
volume={39}
}
In this article, we study numerical approximation of eigenvalue problems of the Schrodinger operator $-\Delta u + \frac{c^2}{|x|^2}u$. There are three stages in our investigation: We start from a ball of any dimension, in which case the exact solution in the radial direction can be expressed by Bessel functions of fractional degrees. This knowledge helps us to design two novel spectral methods by modifying the polynomial basis to fit the singularities of the eigenfunctions. At the second stage… CONTINUE READING
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