Real analyticity away from the nucleus of pseudorelativistic Hartree-Fock orbitals

Details Real analyticity away from the nucleus of pseudorelativistic Hartree-Fock orbitals Real analyticity away from the nucleus of pseudorelativistic Hartree-Fock orbitals

2011-03-25

arxiv.org/abs/1103.5026v2

Physics

Mathematical Physics

44 pages; 2 figures. (1) The result is now extended to the multiconfiguration case (see Remark 1.2 and Theorem 1.3). (2) Ack

Scientific paper

We prove that the Hartree--Fock orbitals of pseudorelativistic atoms, that is, atoms where the kinetic energy of the electrons is given by the pseudorelativistic operator sqrt{-Delta+1}-1, are real analytic away from the origin. As a consequence, the quantum mechanical ground state of such atoms is never a Hartree-Fock state. Our proof is inspired by the classical proof of analyticity by nested balls of Morrey and Nirenberg. However, the technique has to be adapted to take care of the non-local pseudodifferential operator, the singularity of the potential at the origin, and the non-linear terms in the equation.

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