Variational methods in relativistic quantum mechanics
This review is devoted to the study of stationary solutions of linear and nonlinear equations
from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as …
from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as …
The Scott conjecture for large Coulomb systems: a review
We review some older and more recent results concerning the energy and particle
distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic …
distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic …
Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation
According to Dirac's ideas, the vacuum consists of infinitely many virtual electrons which
completely fill up the negative part of the spectrum of the free Dirac operator D 0. In the …
completely fill up the negative part of the spectrum of the free Dirac operator D 0. In the …
Hartree--Fock Theory, Lieb's Variational Principle, and their Generalizations
V Bach - arXiv preprint arXiv:2209.10189, 2022 - arxiv.org
Hartree--Fock theory in quantum mechanics is reviewed, from the proposal of the Hartree--
Fock approximation right after quantum mechanics was formulated to its applications in …
Fock approximation right after quantum mechanics was formulated to its applications in …
Application of the complex-coordinate rotation to the relativistic Hylleraas-CI method: a case study
It is shown that variational solutions corresponding to the bound states of the Dirac–
Coulomb (DC) eigenvalue problem may be obtained using a complex-coordinate rotation …
Coulomb (DC) eigenvalue problem may be obtained using a complex-coordinate rotation …
A new definition of the Dirac–Fock ground state
E Séré - Communications in Mathematical Physics, 2023 - Springer
Abstract The Dirac–Fock (DF) model replaces the Hartree–Fock (HF) approximation in
quantum chemistry when relativistic effects cannot be neglected. Since the Dirac operator is …
quantum chemistry when relativistic effects cannot be neglected. Since the Dirac operator is …
A rigorous justification of the Mittleman's approach to the Dirac–Fock model
L Meng - Calculus of Variations and Partial Differential …, 2024 - Springer
In this paper, we study the relationship between the Dirac–Fock model and the electron-
positron Hartree–Fock model. We justify the Dirac–Fock model as a variational …
positron Hartree–Fock model. We justify the Dirac–Fock model as a variational …
On the Hartree-Fock equations of the electron-positron field
JM Barbaroux, W Farkas, B Helffer… - … in mathematical physics, 2005 - Springer
We study the energy of relativistic electrons and positrons interacting via the second
quantized Coulomb potential in the field of a nucleus of charge Z within the Hartree-Fock …
quantized Coulomb potential in the field of a nucleus of charge Z within the Hartree-Fock …
Unique solutions to Hartree–Fock equations for closed shell atoms
M Griesemer, F Hantsch - Archive for Rational Mechanics and Analysis, 2012 - Springer
In this paper we study the problem of uniqueness of solutions to the Hartree and Hartree–
Fock equations of atoms. We show, for example, that the Hartree–Fock ground state of a …
Fock equations of atoms. We show, for example, that the Hartree–Fock ground state of a …
Existence of minimizers for the Dirac–Fock model of crystals
Whereas many different models exist in mathematics and physics for the ground states of
non-relativistic crystals, the relativistic case has been much less studied, and we are not …
non-relativistic crystals, the relativistic case has been much less studied, and we are not …