University of Sussex
Browse
aa-20170728.pdf (463.31 kB)

Ground state solutions to Hartree–Fock equations with magnetic fields

Download (463.31 kB)
journal contribution
posted on 2023-06-09, 07:54 authored by C Argaez, Michael MelgaardMichael Melgaard
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 $Z_{\rm tot}$ of the nuclei $K$ exceeds $N-1$, where $N$ is the number of electrons. For the first case, the Schr\"{o}dinger 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 $Z_{\rm tot} \a^{2} \leq 0.041$, where $\a$ is the fine structure constant.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Applicable Analysis

ISSN

0003-6811

Publisher

Taylor & Francis

Issue

14

Volume

97

Page range

2377-2403

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Analysis and Partial Differential Equations Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-09-14

First Open Access (FOA) Date

2017-12-12

First Compliant Deposit (FCD) Date

2017-12-12

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC