36 citations · 116 across the 11 of their papers we have counts for
11 papers
Pointwise estimates on derivatives of Coulombic wave functions and their electron densities
Søren Fournais, Thomas Østergaard Sørensen
We prove a priori bounds for all derivatives of non-relativistic Coulombic eigenfunctions, involving negative powers of the distance to the singularities of the many-body potential…
Coulomb potentials and Taylor expansions in Time-Dependent Density Functional Theory
Søren Fournais, Jonas Lampart, Mathieu Lewin +1
We investigate when Taylor expansions can be used to prove the Runge-Gross Theorem, which is at the foundation of Time-Dependent Density Functional Theory (TDDFT). We start with a…
Real analyticity of solutions to Schrödinger equations involving fractional Laplacians
Anna Dall'Acqua, Søren Fournais, Thomas Østergaard Sørensen +1
We prove analyticity of solutions in , , to certain nonlocal linear Schrödinger equations with analytic potentials.
Real analyticity away from the nucleus of pseudorelativistic Hartree-Fock orbitals
Anna Dall'Acqua, Søren Fournais, Thomas Østergaard Sørensen +1
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{-Del…
The relativistic Scott correction for atoms and molecules
Jan Philip Solovej, Thomas Østergaard Sørensen, Wolfgang L. Spitzer
We prove the first correction to the leading Thomas-Fermi energy for the ground state energy of atoms and molecules in a model where the kinetic energy of the electrons is treated…
Hartree-Fock theory for pseudorelativistic atoms
Anna Dall'Acqua, Thomas Østergaard Sørensen, Edgardo Stockmeyer
We study the Hartree-Fock model for pseudorelativistic atoms, that is, atoms where the kinetic energy of the electrons is given by the pseudorelativistic operator \sqrt{(pc)^2+(mc^…
Positivity and lower bounds to the decay of the atomic one-electron density
Søren Fournais, Maria Hoffmann-Ostenhof, Thomas Hoffmann-Ostenhof +1
We investigate properties of the spherically averaged atomic one-electron density rho~(r). For a rho~ which stems from a physical ground state we prove that rho~ > 0. We also give…
Third derivative of the one-electron density at the nucleus
Søren Fournais, Maria Hoffmann-Ostenhof, Thomas Østergaard Sørensen
We study electron densities of eigenfunctions of atomic Schroedinger operators. We prove the existence of rho~'''(0), the third derivative of the spherically averaged atomic densit…
On the convergence of eigenfunctions to threshold energy states
Thomas Østergaard Sørensen, Edgardo Stockmeyer
We prove the convergence in certain weighted spaces in momentum space of eigenfunctions of H = T-lambda*V as the energy goes to an energy threshold. We do this for three choices of…
Non-isotropic cusp conditions and regularity of the electron density of molecules at the nuclei
Søren Fournais, Maria Hoffmann-Ostenhof, Thomas Hoffmann-Ostenhof +1
We investigate regularity properties of molecular one-electron densities rho near the nuclei. In particular we derive a representation rho(x)=mu(x)*(e^F(x)) with an explicit functi…
The large-Z behaviour of pseudo-relativistic atoms
Thomas Østergaard Sørensen
In this paper we study the large-Z behaviour of the ground state energy of atoms with electrons having relativistic kinetic energy sqrt(p^2c^2+m^2c^4)-mc^2. We prove that to leadin…