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PHY.K02UF Molecular and Solid State Physics

## Introduction

Solid state physics relates the microscopic structure of a solid (the arrangement of the atoms) to its macroscopic properties (density, strength, electrical conductivity, thermal conductivity, optical properties, magnetism, color, etc.). Early in the history of solid state physics, basic properties of solids like density, color, hardness or yield strength were measured experimentally and tabulated. Experimental observations were used to formulate phenomenological laws. For instance, it is observed that the current that flows through a metal resistor is proportional to the voltage applied. From this observation Ohm postulated his phenomenological law, $V=IR$ (Voltage = Current* Resistance) without any deeper theoretical understanding.

As time went on and our theoretical understanding of solids improved, it became clear that every property of a solid can be calculated from the Schrödinger equation. This equation tells us which microscopic arrangement of the atoms in a solid has the lowest energy as well as the electrical, thermal, and optical properties of this arrangement of atoms. The only problem with this approach is that the Schrödinger equation is devilishly difficult to solve for many particle problems such as finding the quantum states for all electrons, protons, and neutrons in a solid.

In this course, approximations are introduced that make the Schrödinger equation easier to solve. In the section on molecules, sometimes we will neglect the electron-electron interactions which makes the Schrödinger equation much easier to solve. In the section on molecules we go further and neglect the electron-nuclei interactions as well as the electron-electron interactions. This results in the the famous "free electron model" is widely used to approximate the properties of metals and semiconductors. From this simple model, properties like the specific heat or the electrical conductivity can be calculated.

The lectures do not closely follow a book for the sections on atoms or molecules. There are online notes that can be found by following the links in the course outline. A longer explanation of these topics can be found in: Experimentalphysik 3: Atome, Moleküle und Festkörper by Demtröder, The Physics of Atoms and Quanta by H. Haken and H. C. Wolf, and Molecular Physics & Elementary of Quantum Chemistry, H. Haken un H. C. Wolf. See the section on text books for links to online versions of these books in German.

In the section of the course about solids, the lectures most closely follow Introduction to Solid State Physics by Charles Kittel. Other books that cover almost the same material are: Festkörperphysik by R. Gross and A. Marx, and Festkörperphysik by H. Ibach and H. Lüth. These books are also available online in the list of text books.

As part of the exercises that go with these lectures, every student must contribute something that will improve the course. This contribution should correspond to about 4 hours of work. It can be anything that you think will help students pass the exam. There is a list of suggested projects.