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Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms

Marcel Griesemer
(Universität Stuttgart)
Mat/Fys-seminar
Tirsdag, 27 september, 2011, at 15:15-16:15, in Aud. G2 (1532-122)
Abstrakt:
This talk is devoted to the problem of uniqueness of solutions to the Hartree and the Hartree-Fock equations of atoms. I will explain, for example, that the Hartree-Fock ground state of a closed shell atom is unique provided the atomic number $Z$ is sufficiently large compared to the number $N$ of electrons. More specifically , a two-electron atom with atomic number $Z\geq 35$ has a unique ground state given by two orbitals with opposite spins and identical spatial wave functions. This statement is wrong for some $Z>1$. which exhibits a phase segregation.