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