Abstract.
We study electron densities of eigenfunctions of atomic Schrödinger operators. We prove the existence of \(\tilde{\rho}^{\prime\prime\prime}(0)\), the third derivative of the spherically averaged atomic density \(\tilde{\rho}\)at the nucleus. For eigenfunctions with corresponding eigenvalue below the essential spectrum in any symmetry subspace we obtain the bound \(\tilde{\rho}^{\prime\prime\prime}(0)\leq -(7/12)Z^{3}{\tilde{\rho}}(0)\), where Z denotes the nuclear charge. This bound is optimal.
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Communicated by Claude Alain Pillet.
© 2008 by the authors. This article may be reproduced in its entirety for non-commercial purposes.
Submitted: April 22, 2008. Accepted: July 7, 2008.
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Fournais, S., Hoffmann-Ostenhof, M. & Sørensen, T.Ø. Third Derivative of the One-Electron Density at the Nucleus. Ann. Henri Poincaré 9, 1387–1412 (2008). https://doi.org/10.1007/s00023-008-0390-8
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DOI: https://doi.org/10.1007/s00023-008-0390-8