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Condensed Matter Theory I: The complexity of 1023 particles interacting with each other in a solid give rise to many emergent phenomena one would not predict from the simple interactions between two electrons. In this lecture we will, starting from simple models and theories work our way into the contemporary theory of many particle physics. The lecture follows for a large part the textbook of Ashcroft and Mermin, with one big difference. The aforementioned text-book is based on a text over 50 years old. During the last decades new methods have emerged, often removing the need to know the full wave-function of the system to answer the problem, by using Green's functions. Whenever possible the later will be used within this lecture. Concepts of many particle systems discused are: The Drude Theory of Metals The Sommerfeld Theory of Metals Electrons in a periodic potential Tight binding Band-structure, Fermi-surface, Density of states, Metals, Insulators, Semiconductors Semiconductor physics Surface states Phonons and disorder Relativistic corrections - spin-orbit coupling Phase transitions and topology Response functions Theoretical / Mathematical tools used will be Second quantization Green's functions (on an independent particle level) Self energy (for surface states and disorder) Levels of theory discussed will be Mean-field theory Hartree-Fock Density functional theory
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