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arXiv · 1910.01925

One-Dimensional Lieb-Oxford Bounds

Andre Laestadius·Fabian M Faulstich
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Abstract

We investigate and prove Lieb-Oxford bounds in one dimension by studying convex potentials that approximate the ill-defined Coulomb potential. A Lieb-Oxford inequality establishes a bound of the indirect interaction energy for electrons in terms of the one-body particle density $\rho_\psi$ of a wave function $\psi$. Our results include modified soft Coulomb potential and regularized Coulomb potential. For these potentials, we establish Lieb-Oxford-type bounds utilizing logarithmic expressions of the particle density. Furthermore, a previous conjectured form $I_\mathrm{xc}(\psi)\geq - C_1 \int_{\mathbb R} \rho_\psi(x)^{2} \mathrm{d}x$ is discussed for different convex potentials.

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BibTeXRIS

Andre Laestadius, Fabian M Faulstich. 2019-10-04. One-Dimensional Lieb-Oxford Bounds. https://doi.org/10.1063/5.0009419

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