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Real analyticity away
from the nucleus of pseudorelativistic Hartree–Fock
orbitals
Anna Dall’Acqua, Søren Fournais, Thomas Østergaard Sørensen and Edgardo Stockmeyer |
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Vol. 5 (2012), No. 3, 657–691
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Abstract |
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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 , 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
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Mathematical Subject Classification 2010
Primary: 35B65, 35J10, 81Q05, 81V55
Secondary: 81V70, 35Q40
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Milestones
Received: 28 March 2011
Accepted: 28 August 2011
Published: 15 October 2012
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Authors |
| Anna Dall’Acqua | |
| Institut für Analysis und Numerik,
Fakultät für Mathematik Otto-von-Guericke Universität Postfach 4120 D-39106 Magdeburg Germany |
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| 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 |
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