Foundations of Computational Materials Science

# Course Content

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The planned content of the course week by week. In previous years, quantum mechanics preceded classical physics. For a didactic point of view, it has changed.

1. Introduction and Basic Concepts of Classical Statistical Mechanics
2. Statistical Mechanics of Interacting Particle Systems
3. The Boltzmann Equation
4. H Theorem and Thermodynamic Irreversibility

The rest is about quantumphysics

1.   2. Introduction to Quantum Mechanics
3. Quantum and Classical Molecular Dynamics

The rest three sections are about quantum many electron problems

1.   2. Properties of Many-Electron Systems, Hartree-Fock Approximation
3. Free Electron Gas
4. Density Functional Theory

# About

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## What is this

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This note is support the lecture held at FAU by Michael Zaiser. This note is intended to develop collaboratively, therefore if you have any questions or notes (on the grammar, content or anything), feel free to let us know, or edit the page directly. The idea is to make this content better year by year (starting date is 2015), for what it is desirable to have feedback from the audience.

The purpose of this note is to better understand the slides shown during the lectures, and include more content, for what time is not always available. This note is intended to be complete, i.e. the whole lecture could be understood based on only this source.

The basis of this material is the slides of the course, extended with lecture notes and further sources. It is not guaranteed that all the material here is correct, some of them may not even seen by any kind of lector.

## Course organisation

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* The course language is English
* 2 hours of lectures and tutorials are alternating, exception is the first two weeks, when only lectures are held
* The purpose of tutorials is to deepen conceptual understanding, some tasks containing programming and numeric solutions or analytical work.

## How to use this?

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To display equations in a better way,

* For Firefox users, install the [MathML-fonts]
* For Chrome users, install [MathJax addon]

and then set the Preferences -> Appearance -> Math to 'MathML with SVG or PNG fallback'.

Here are two examples:

1. The N-particle density function is  ρ ( r 1 , r 2 , . . . , r n , p 1 , p 2 , . . . , p n ) {\displaystyle \rho \left({{\mathbf {r} }_{1}},{{\mathbf {r} }_{2}},...,{{\mathbf {r} }_{n}},{{\mathbf {p} }_{1}},{{\mathbf {p} }_{2}},...,{{\mathbf {p} }_{n}}\right)} where  r i {\displaystyle {{\mathbf {r} }_{i}}} is the position and  p i {\displaystyle {{\mathbf {p} }_{i}}} is the impulse of the ith particle.
2. Another example from complex calculus:  f ( a ) = 1 2 π i ∮ γ f ( z ) z − a d z {\displaystyle f\left(a\right)={\frac {1}{2\pi i}}\oint _{\gamma }{{\frac {f\left(z\right)}{z-a}}dz}}