## 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 nonrelativistic 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, specialized models will be introduced that are designed which make the Schrödinger equation relatively easy to solve. For instance, the famous "free electron model" is widely used to approximate the properties of metals and semiconductors. Starting from a simplified model, it is often possible to understand trends in the tabulated experimental data or to reproduce results described by a simple phenomenological law.

For some phenomena, like the Quantum Hall Effect, superconductivity, or magnetism, there is no alternative but to start with the many particle Schrödinger equation and find its solutions.