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

• DOI: 10.2140/apde.2012.5.657
• Publication Date: 2012-11-02T09:02:57Z
• Authors: Anna Dall’Acqua; Søren Fournais; Thomas Østergaard...; Edgardo Stockmeyer
• Keywords: pseudorelativistic; Hartree–Fock model; 35B65; Hartree-Fock model; 35J10; FOS: Physical sciences; regularity of wavefunctions; 35B65, 35J10, 81Q05, 81V55, 81V70, 35Q40; Mathematical Physics (math-ph); 01 natural sciences; 81Q05; 81V55; Mathematics - Analysis of PDEs; 35Q40; 03 Salud y bienestar; real analyticity; 81V70; FOS: Mathematics; 03 Good Health and Well-being; 0101 mathematics; Mathematical Physics; nonlocal operator; Analysis of PDEs (math.AP)

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