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Ground state solutions to Hartree–Fock equations with magnetic fields
journal contribution
posted on 2023-06-09, 07:54 authored by C Argaez, Michael MelgaardMichael MelgaardWithin 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.
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Publication status
- Published
File Version
- Accepted version
Journal
Applicable AnalysisISSN
0003-6811Publisher
Taylor & FrancisExternal DOI
Issue
14Volume
97Page range
2377-2403Department 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
2017-09-14First Open Access (FOA) Date
2017-12-12First Compliant Deposit (FCD) Date
2017-12-12Usage metrics
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