Existence of infinitely many distinct solutions to the quasi-relativistic Hartree-Fock equations

Enstedt, M and Melgaard, M (2009) Existence of infinitely many distinct solutions to the quasi-relativistic Hartree-Fock equations. International Journal of Mathematics and Mathematical Sciences, 2009. pp. 1-20. ISSN 0161-1712

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Abstract

We establish existence of infinitely many distinct solutions to the Hartree-Fock equations for Coulomb systems with quasi-relativistic kinetic energy $\sqrt{ -\a^{-2} D_{x_{n}} + \a^{-4}} -\a^{-2}$ for the $n^{\rm th}$ electron. Moreover, we prove existence of a ground state. The results are valid under the hypotheses that the total charge $Z_{\rm tot}$ of $K$ nuclei is greater than or equal to the total number of electrons $N$ and that $Z_{\rm tot}$ is smaller than some critical charge $Z_{\rm c}$. The proofs are based on critical point theory in combination with density operator techniques.

Item Type: Article School of Mathematical and Physical Sciences > Mathematics Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems Richard Chambers 20 May 2013 15:03 24 Jun 2013 08:47 http://sro.sussex.ac.uk/id/eprint/44777