The lecture notes here were prepared during the Summer of 2024 when me and my friends studied the subjects of the course beforehand. The contents of this lecture note have been compiled from the lecture notes of our friends who took this course before us, the main textbook of the course, and the lecture notes of Prof. Hande Toffoli. 

The course Phys 430 - Statistical Thermodynamics was given by Prof. Altan Baykal and included the following topics in order: 

• The First Law of Thermodynamics. Functions of State, Thermodynamic Functions

• Entropy. The Carnot Cycle, Approach to Equilibrium, Second Law of Thermodynamics

• Probability and Statistics. Axioms of Probability Theory, Distributions

• Ideas of Statistical Mechanics. Boltzmann Entropy

• The Canonical Ensemble. Partition Function, Rotational and Vibrational Degrees of Freedom, Equipartition Theorem

• Identical Particles. Bosons, Fermions, Spin Degrees of Freedom

• Maxwell Distribution of Speeds

• Planck's Distribution. Einstein and Debye Models of Vibrations in Solids, Solids and Vapours in Equilibrium 

• Systems with Variable Numbers of Particles. Chemical Potential, Grand Canonical Ensemble, Grand Potential

• Fermi and Bose Particles. Fermi Gas, Non-Interacting Bose Gas, Bose-Einstein Condensates.

Given by Prof. Gürsevil Turan, the course Phys 431 - Quantum Mechanics includes the following topics in order:

• Angular Momentum. Ladder Operators, Spherical Coordinates, Eigenvalues and Eigenfunctions of Angular Momentum, Spherical Harmonics

• Schrödinger Equation in Three Dimensions. SE in Cartesian Coordinates, SE in Spherical Coordinates, 

• The Hydrogen Atom. Wave Functions of the Hydrogen Atom, Degeneracy of the Bound States, Properties of the Hydrogen Atom, Hydrogen Spectra

• Spin. Pauli Matrices and Spinors, Spin Wavefunctions, Stern-Gerlach Experiment

• Addition of Angular Momentum. Uncoupled and Coupled Representations, Clebsch-Gordan Coefficients

• Time-Independent Perturbation Theory. Degenerate Perturbation Theory, Stark Effect, Fine Structure of the Hydrogen Atom, Relativistic Corrections and the Spin-Orbit Coupling