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Existence of a solution to Hartree-Fock equations with decreasing magnetic fields. (English) Zbl 1145.81445

Summary: 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 \(Z\) of \(K\) nuclei exceeds \(N - 1\), where \(N\) is the number of electrons. In the opposite direction, no ground state exists if \(N>2Z+K\).

MSC:

81V55 Molecular physics
35Q40 PDEs in connection with quantum mechanics
47G20 Integro-differential operators
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35Q75 PDEs in connection with relativity and gravitational theory
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