Mathematics Commons^™

Abstract Criteria For Multiple Solutions To Nonlinear Coupled Equations Involving Magnetic Schrodinger Operators, Mattias Enstedt, Michael Melgaard

Articles

We consider a system of nonlinear coupled equations involving magnetic Schrodinger

operators and general potentials. We provide a criteria for the existence of multiple

solutions to these equations. As special cases we get the classical results on

existence of innitely many distinct solutions within Hartree and Hartree-Fock

theory of atoms and molecules subject to an external magnetic fields. We also

extend recent results within this theory, including Coulomb system with a constant

magnetic field, a decreasing magnetic field and a "physically measurable" magnetic field.

Existence Of A Solution To Hartree-Fock Equations With Decreasing Magnetic Field, Mattias Enstedt, Michael Melgaard

Articles

In the presence of an external magnetic field, we prove existence of a ground state within the Hartree–Fock theory of atoms and molecules. The ground state exists provided the magnetic field decreases at infinity and the total charge of nuclei exceeds , where is the number of electrons. In the opposite direction, no ground state exists if .