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From atoms to crystals: a mathematical journey (Q5461288)

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scientific article; zbMATH DE number 2188193

Language	Label	Description	Also known as
English	From atoms to crystals: a mathematical journey	scientific article; zbMATH DE number 2188193

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scholarly article

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From atoms to crystals: a mathematical journey (English)

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zbMATH Open document ID

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10.1090/S0273-0979-05-01059-1

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Pierre-Louis Lions

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Bulletin of the American Mathematical Society

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publication date

26 July 2005

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Mathematics Subject Classification ID

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zbMATH DE Number

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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HANS BETHE'S CONTRIBUTIONS TO SOLID-STATE PHYSICS

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Convergent iterative methods for the Hartree eigenproblem

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Error bound for the Hartree-Fock energy of atoms and molecules

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Mean field dynamics of fermions and the time-dependent Hartree-Fock equation

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Regularity in a Schrödinger equation with a potential singular at finite distance and at infinity

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Regularity for a Schrödinger equation with singular potentials and application to bilinear optimal control

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The Thomas-Fermi-von Weizsäcker theory of atoms and molecules

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Sharp condition on the decay of the potential for the absence of a zero-energy ground state of the Schrodinger equation

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A Nonlinear Elliptic System Arising in Electron Density Theory

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GEOMETRY OPTIMIZATION FOR CRYSTALS IN THOMAS–FERMI TYPE THEORIES OF SOLIDS

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Optimisation de géométrie dans le cadre des théories de type Thomas—Fermi pour les cristaux périodiques

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A definition of interface energies using atomistic models.

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Thomas-Fermi type theories for polymers and thin films.

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Periodicity of the infinite-volume ground state of a one-dimensional quantum model

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From molecular models to continuum mechanics

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A Definition of the Ground State Energy for Systems Composed of Infinitely Many Particles

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Convergence de modèles moléculaires vers des modèles de mécanique des milieux continus

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Characterization of functions on \(\mathbb{R}^3\) with bounded Newtonian potential

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Mathematical methods in physics. Distributions, Hilbert space operators, variational methods, and applications in quantum physics

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A DECOMPOSITION THEOREM FOR WAVE FUNCTIONS IN MOLECULAR QUANTUM CHEMISTRY

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Deformations of density functions in molecular quantum chemistry

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A mathematical investigation of the Car-Parrinello method

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Homogenization in time of singularly perturbed mechanical systems

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Density matrices in \(O(N)\) electronic structure calculations: theory and applications

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Electronic wave functions - I. A general method of calculation for the stationary states of any molecular system

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NON-LOCAL VARIATIONAL LIMITS OF DISCRETE SYSTEMS

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Continuum Limits of Discrete Systems without Convexity Hypotheses

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Semilinear equations in \({\mathbb{R}}^ N\) without condition at infinity

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ON THE PERTURBATION METHODS FOR SOME NONLINEAR QUANTUM CHEMISTRY MODELS

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ON THE TIME-DEPENDENT HARTREE–FOCK EQUATIONS COUPLED WITH A CLASSICAL NUCLEAR DYNAMICS

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On the convergence of SCF algorithms for the Hartree-Fock equations

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Contrôle optimal bilinéaire d'une équation de Schrödinger

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INTEGRAL EQUATION METHODS FOR MOLECULAR SCALE CALCULATIONS IN THE LIQUID PHASE

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QUANTUM MONTE CARLO SIMULATIONS OF FERMIONS: A MATHEMATICAL ANALYSIS OF THE FIXED-NODE APPROXIMATION

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On some periodic Hartree-type models for crystals

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Sur la limite thermodynamique pour des modèles de type Hartree et Hartree-Fock

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Binding of atoms and stability of molecules in hartree and thomas-fermi type theories.

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Binding of atoms and stability of molecules in hartree and thomas-fermi type theories.

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Global existence of solutions to the Cauchy problem for time-dependent Hartree equations

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Reduced density matrices. Coulson's challenge

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An introduction to \(\Gamma\)-convergence

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Numerical Solution of the Schrödinger Equation in a Wavelet Basis for Hydrogen-like Atoms

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Computing a molecule: A mathematical viewpoint

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Mathematical models and methods for ab initio quantum chemistry

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Variational characterization for eigenvalues of Dirac operators

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On the eigenvalues of operators with gaps. Application to Dirac operators

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An analytical proof of Hardy-like inequalities related to the Dirac operator

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Stationary states of the nonlinear Dirac equation: A variational approach

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Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations

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Bound-state solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac systems

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Solutions of the Dirac-Fock equations for atoms and molecules

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An overview on linear and nonlinear Dirac equations

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Nonrelativistic limit of the Dirac-Fock equations

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The atomic and molecular nature of matter

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On the energy of a large atom

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On the Dirac and Schwinger corrections to the ground-state energy of an atom

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Analyticity of the density of electronic wavefunctions

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The electron density is smooth away from Nuclei

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The multiconfiguration equations for atoms and molecules: charge quantization and existence of solutions

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A scheme for the passage from atomic to continuum theory for thin films, nanotubes and nanorods

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Validity and failure of the Cauchy-Born hypothesis in a two-dimensional mass-spring lattice

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Hartree-Fock theory in nuclear physics

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Thomas-Fermi theory with magnetic fields and the Fermi-Amaldi correction

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Mathematical concepts of quantum mechanics.

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A time dependent Born-Oppenheimer approximation

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Electron wavefunctions and densities for atoms

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The quantum N-body problem

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On the Schrödinger equation with time-dependent electric fields

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Electronic structure calculations for plane-wave codes without diagonalization

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On the eigenfunctions of many-particle systems in quantum mechanics

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Perturbation theory for linear operators.

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Handbook of Numerical Analysis X. Special volume: Computational chemistry.

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Some results on the Thomas-Fermi-Dirac-von Weizsäcker model

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A general approach for multiconfiguration methods in quantum molecular chemistry

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On the spin polarized thomas-fermi model with the fermi-amaldi correction

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Computational chemistry from the perspective of numerical analysis

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The multiconfiguration methods in quantum chemistry: Palais-Smale condition and existence of minimizers.

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Solutions of the multiconfiguration equations in quantum chemistry

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The stability of matter: from atoms to stars

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The Thomas-Fermi theory of atoms, molecules and solids

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Thomas-fermi and related theories of atoms and molecules

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Equilibrium statistical theory for nearly parallel vortex filaments

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Solutions of Hartree-Fock equations for Coulomb systems

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The concentration-compactness principle in the calculus of variations. The limit case. II

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The concentration-compactness principle in the calculus of variations. The locally compact case. I

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Error bars and quadratically convergent methods for the numerical simulation of the Hartree-Fock equations

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A simple model for phase transitions: from the discrete to the continuum problem

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Solutions of the Dirac-Fock equations without projector.

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Universality in the Thomas-Fermi-von Weizsäcker model of atoms and molecules

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Proof of the ionization conjecture in a reduced Hartree-Fock model

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The relativistic interaction of two electrons in the self-consistent field method

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On the regularity of the electronic Schrödinger equation in Hilbert spaces of mixed derivatives

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Sparse grid spaces for the numerical solution of the electronic Schrödinger equation

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full work available at URL

https://doi.org/10.1090/s0273-0979-05-01059-1

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Mathematics(1 entry)

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