A quantum mechanical equation H Ψ= E Ψ is composed of three components, viz.,
Hamiltonian H, wave function Ψ, and property E (λ), each of which is confronted with …

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 …

Relativistic effects are of major importance for understanding the properties of heavier atoms
and molecules. Volumes I-III of Relativistic Theory of Atoms and Molecules constitute the …

This article is concerned with the derivation and the mathematical study of a new mean-field
model for the description of interacting electrons in crystals with local defects. We work with …

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 …

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 …

Introduction to Representations of the Canonical Commutation and Anticommutation Relations
Page 1 Introduction to Representations of the Canonical Commutation and Anticommutation …

We study the mean‐field approximation of quantum electrodynamics (QED) by means of a
thermodynamic limit. The QED Hamiltonian is written in Coulomb gauge and does not …

The Hartree-Fock ground state of a homogeneous electron gas is never translation invariant,
even at high densities. As proved by Overhauser, the (paramagnetic) free Fermi gas is …

A polaron is an electron interacting with a polar crystal, which is able to form a bound state
by using the distortions of the crystal induced by its own density of charge. In this paper we …