X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Fthesis%2Fbasics.tex;h=8ab5002715fe796e75e78a2a78ad2c3b3db94976;hp=b1beb7f85c762f2cc72b36ae804f96c072285229;hb=7340b277821e2725d1f47f7d1cf230a7a1b0a943;hpb=6b8e82e926099b05e961285bb4307711d1aa8d3e

diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex
index b1beb7f..8ab5002 100644
--- a/posic/thesis/basics.tex
+++ b/posic/thesis/basics.tex
@@ -277,18 +277,16 @@ It provides a stable algorithm that allows smooth changes of the system to new v
 \section{Denstiy functional theory}
 \label{section:dft}
 
-In quantum-mechanical modeling the problem of describing a many-body problem is manifested in the high-dimensional Schr\"odinger equation for the wave function $\Psi({\vec{R}},{\vec{r}})$ that depends on the coordinates of the nuclei and electrons.
+In quantum-mechanical modeling the problem of describing the many-body problem, i.e. a system of a large amount of interacting particles, is manifested in the high-dimensional Schr\"odinger equation for the wave function $\Psi({\vec{R}},{\vec{r}})$ that depends on the coordinates of all nuclei and electrons.
 The Schr\"odinger equation contains the kinetic energy of the ions and electrons as well as the electron-ion, ion-ion and electron-electron interaction.
 This cannot be solved exactly and there are several layers of approximations to reduce the number of parameters.
-In density functional theory (DFT) the problem is recasted to the charge density $n(\vec{r})$ instead of using the description by a wave function.
+The key point in density functional theory (DFT) is to recast the problem to a description using the charge density $n(\vec{r})$ that depends on only three spatial coordinates instead of the many-body wave function.
 Formally DFT can be regarded as an exactification of both, the Thomas Fermi and Hartree theory.
-
-Since {\textsc vasp} \cite{kresse96} is used in this work, theory and implementation of sophisticated algorithms of DFT codes is not subject of this work.
-Thus, the content of the following sections is restricted to the very basic idea of DFT.
+In the following sections the basic idea of DFT will be outlined.
 
 \subsection{Born-Oppenheimer approximation}
 
-The first approximation ...
+The first approximation employed 
 
 \subsection{Hohenberg-Kohn theorem}