Related papers: Wavefunctions for large systems as basis for elect…
Wavefunctions for large electron numbers suffer from an exponential growth of the Hilbert space which is required for their description. In fact, as pointed out by W. Kohn, for electron numbers $N > N_0$ where $N_0 \approx 10^3$ they become…
The dimension of the Hilbert space needed for the description of an interacting electron system increases exponentially with electron number $N$. As pointed out by W. Kohn this exponential wall problem (EWP) limits the concept of…
An alternative to Density Functional Theory are wavefunction based electronic structure calculations for solids. In order to perform them the Exponential Wall (EW) problem has to be resolved. It is caused by an exponential increase of the…
The Bloch wavefunction leads either to mathematically impossible consequences or suggests that the ground state energy is a function of size and shape when the geometry of large crystals is considered in detail. It is incompatible with the…
A new iterative solver is proposed to efficiently calculate the ground state electronic structure in Density Functional Theory calculations. This algorithm is particularly useful for simulating physical systems considered difficult to…
Wavefunctions for large electron numbers $N$ are plagued by the Exponential Wall Problem (EWP), i.e., an exponential increase in the dimensions of Hilbert space with $N$. Therefore they loose their meaning for macroscopic systems, a point…
We formulate the calculation of the ground-state wavefunction and energy of a system of strongly correlated electrons in terms of scattering matrices. A hierarchy of approximations is introduced which results in an incremental expansion of…
This chapter introduces the main ideas and the most important methods for representing the electronic wavefunction through machine learning models. The wavefunction of a N-electron system is an incredibly complicated mathematical object,…
A number of methods are discussed which may serve for a treatment of electron correlations in solids. When the electron correlations are relatively weak like in semiconductors or a number of ionic crystals one may start from a…
The Hilbert space for an interacting electron system increases exponentially with electron number $N$. This limits the concept of wavefunctions $\psi$ based on solutions of the Schr\"odinger equation to $N \leq N_0$ with $N_0 \simeq 10^3$…
For molecules and solids containing heavy elements, accurate electronic structure calculations require accounting not only for electronic correlations but also for relativistic effects. In molecules, relativity can lead to severe changes in…
We present a review of the basic ideas and techniques of the spectral density functional theory which are currently used in electronic structure calculations of strongly-correlated materials where the one-electron description breaks down.…
A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layer structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to…
Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries…
Wavefunction forms based on products of electron pairs are usually constructed as closed-shell singlets, which is insufficient when the molecular state has a nonzero spin or when the chemistry is determined by $d$- or $f-$electrons. A set…
Multiresolution analysis of electronic structure affords the opportunity to capture the full physics of atomic cores in a systematically improvable manner. Applying new techniques, we demonstrate for the first time that multiresolution…
This article reviews recent developments in multiresolution analysis which make it a powerful tool for the systematic treatment of the multiple length-scales inherent in the electronic structure of matter. Although the article focuses on…
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
The electron structure functions are studied in polarized $e^+e^-$ scattering. The formulae for longitudinally and transversely polarized electrons are presented. The smallnes of the electron mass leads to negligible cross-sections and…
The electron and photon structure functions are compared. Advantages of the electron structure function are demonstrated. At very high momenta probabilistic (partonic) interpretation can be preserved despite strong $\gamma$-$Z$…