The difference equation related to the problem of the hydrogen atom in a strong magnetic field.
The energy of heavy atoms according to Brown and Ravenhall: the Scott correction.
The ground state energy of relativistic one-electron atoms according to Jansen and Heß.
The mathematics of large atoms
The mixed regularity of electronic wave functions multiplied by explicit correlation factors
The electronic Schrödinger equation describes the motion of N electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3N variables, three spatial dimensions for each electron. Approximating them is thus inordinately challenging. As is shown in the author's monograph [Yserentant, Lecture Notes in Mathematics 2000, Springer (2010)], the regularity of the solutions, which increases with the number of electrons,...
The mixed regularity of electronic wave functions multiplied by explicit correlation factors***
The electronic Schrödinger equation describes the motion of N electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3N variables, three spatial dimensions for each electron. Approximating them is thus inordinately challenging. As is shown in the author's monograph [Yserentant, Lecture Notes in Mathematics2000, Springer (2010)], the regularity of the solutions, which increases with the number of electrons,...
The projected single-particle Dirac operator for Coulombic potentials.
The spin of the ground state of an atom.
In this paper we address a question posed by M. and T. Hoffmann-Ostenhof, which concerns the total spin of the ground state of an atom or molecule. Each electron is given a value for spin, ±1/2. The total spin is the sum of the individual spins.