Ground state solutions to Hartree–Fock equations with magnetic fields

ABSTRACT

Within the Hartree–Fock theory of atoms and molecules, we prove existence of a ground state in the presence of an external magnetic field when: (1) the diamagnetic effect is taken into account; (2) both the diamagnetic effect and the Zeeman effect are taken into account. For both cases, the ground state exists provided the total charge of the nuclei K exceeds , where N is the number of electrons. For the first case, the Schrödinger case, we complement prior results by allowing a wide class of magnetic potentials. In the second case, the Pauli case, we include the magnetic field energy in order to obtain a stable problem and we assume , where is the fine structure constant.

Keywords:

• Ground states
• Hartree–Fock equations
• magnetic fields
• Zeeman effect

Acknowledgements

The authors thank the anonymous referees for their careful reading of the paper and their constructive suggestions. The second author would like to thank Dr. M. Enstedt for several discussions in the early stages of this work.

Notes

No potential conflict of interest was reported by the authors.