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 …
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 …
Some bound state problems in quantum mechanics
D Hundertmark - Proceedings of Symposia in Pure Mathematics, 2007 - books.google.com
We give a review of semi-classical estimates for bound states and their eigenvalues for
Schrödinger operators. Motivated by the classical results, we discuss their recent …
Schrödinger operators. Motivated by the classical results, we discuss their recent …
Hartree–Fock theory for pseudorelativistic atoms
A Dall'Acqua, TØ Sørensen, E Stockmeyer - Annales Henri Poincaré, 2008 - Springer
We study the Hartree–Fock model for pseudorelativistic atoms, that is, atoms where the
kinetic energy of the electrons is given by the pseudo-relativistic operator (|\bf p| c)^ 2+(mc …
kinetic energy of the electrons is given by the pseudo-relativistic operator (|\bf p| c)^ 2+(mc …
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 …
Ground state and charge renormalization in a nonlinear model of relativistic atoms
We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe
relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The …
relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The …
Solutions to quasi-relativistic multi-configurative Hartree–Fock equations in quantum chemistry
C Argaez, M Melgaard - Nonlinear Analysis: Theory, Methods & …, 2012 - Elsevier
We establish the existence of infinitely many distinct solutions to the multi-configurative
Hartree–Fock type equations for N-electron Coulomb systems with quasi-relativistic kinetic …
Hartree–Fock type equations for N-electron Coulomb systems with quasi-relativistic kinetic …