Vol. 5, No. 3, 2012

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Real analyticity away from the nucleus of pseudorelativistic Hartree–Fock orbitals

Anna Dall’Acqua, Søren Fournais, Thomas Østergaard Sørensen and Edgardo Stockmeyer

Vol. 5 (2012), No. 3, 657–691
Abstract

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 Δ + 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 nonlocal pseudodifferential operator, the singularity of the potential at the origin, and the nonlinear terms in the equation.

Keywords
Hartree–Fock model, pseudorelativistic, regularity of wavefunctions, nonlocal operator, real analyticity
Mathematical Subject Classification 2010
Primary: 35B65, 35J10, 81Q05, 81V55
Secondary: 81V70, 35Q40
Milestones
Received: 28 March 2011
Accepted: 28 August 2011
Published: 15 October 2012
Authors
Anna Dall’Acqua
Institut für Analysis und Numerik, Fakultät für Mathematik
Otto-von-Guericke Universität
Postfach 4120
D-39106 Magdeburg
Germany
Søren Fournais
Department of Mathematical Sciences
University of Aarhus
Ny Munkegade 118
DK-8000 Aarhus C
Denmark
CNRS and Laboratoire de Mathématiques d’Orsay
Université Paris-Sud
Orsay Cedex, F-91405
France
Thomas Østergaard Sørensen
Department of Mathematics
Imperial College London
Huxley Building
180 Queen’s Gate
London SW7 2AZ
United Kingdom
Mathematisches Institut
Universität München
Theresienstraße 39
D-80333 Munich
Germany
Edgardo Stockmeyer
Mathematisches Institut
Universität München
Theresienstraße 39
D-80333 Munich
Germany