Table of Contents1 Classical Statistical Mechanics1.1 Kinetic Theory of Gases 1.1.1 Maxwell Distribution of Velocities1.1.2 Maxwell-Boltzmann Distribution of Energies 1.1.3 Single-Particle Density of States 1.2 Statistical Ensembles of Gibbs 1.2.1 Microcanonical Ensemble 1.2.2 Canonical Ensemble 1.2.3 Grand Canonical Ensemble 1.2.4 Many-Particle Density of States 2 Special Relativity 2.1 Lorentz Transformations 2.2 Einstein Postulates 2.2.1 Gedanken Experiment of Einstein 2.3 Relativistic Mechanics 2.3.1 Relativistic Kinematics 2.3.2 Relativistic Dynamics 3 Quantum Properties of Light 3.1 Black-Body Radiation 3.1.1 Ideal Black Body 3.1.2 Derivation of the Planck Law 3.2 Photoelectric E ect 3.2.1 Experimental Data 3.2.2 Theoretical Explanation 3.3 Energy and Linear Momentum of a Photon 3.4 Compton E ect 3.4.1 Theoretical Explanation 4 Quantum Energy Levels of Atoms 4.1 Energy Spectra 4.1.1 Energy Spectrum of Hydrogen Atom 4.2 Hydrogen Atom of Bohr4.2.1 Derivation of the Bohr Results 4.3 Energy Levels and Photons 4.4 Electromagnetic Transitions 5 Wave Properties of Matter 5.1 De Broglie Wavelength 5.1.1 Explaining the Bohr Quantization 5.2 Experiment of Davisson and Germer 5.3 Double-Slit Experiment with Light5.4 Double-Slit Experiment with Electrons 5.5 Old Quantum Mechanics of Bohr, Wilson and Sommerfeld5.6 Matrix Quantum Mechanics of Heisenberg, Born and Jordan 5.7 Wave Quantum Mechanics of Schrodinger 5.7.1 Derivation of the Schr odinger Equation 5.8 Formal Quantization Rules5.8.1 Schrodinger Equation for a Free Particle 5.8.2 Schrodinger Equation for a Particle in an External Potential 5.9 Stationary Schr odinger Equation6 Axioms of Quantum Mechanics 6.1 Matrix Mechanics 6.2 Axioms of Quantum Mechanics7 Applications of Quantum Mechanics 7.1 Quantum Particle in a One-Dimensional Box Potential7.2 Quantum Particle in a One-Dimensional Harmonic Potential8 Quantum Physics of Atoms 8.1 Quantum Particle in a Separable Potential 8.1.1 Quantum Particle in the Harmonic Potential 8.2 Dirac Notation for a Quantum State8.3 Electron in the Hydrogen Atom 8.3.1 Schrodinger Equation in Spherical Polar Coordinates 8.3.2 Selection Rules 8.4 Pauli Exclusion Principle and the Spin8.5 Semi-Integer and Integer Spin: Fermions and Bosons8.6 The Dirac Equation 8.6.1 The Pauli Equation and the Spin8.6.2 Dirac Equation with a Central Potential 8.6.3 Relativistic Hydrogen Atom and Fine Splitting 8.6.4 Relativistic Corrections to the Schrodinger Hamiltonian9 Quantum Mechanics of Many-Body Systems 9.1 Identical Quantum Particles 9.1.1 Spin-Statistics Theorem9.2 Non-Interacting Identical Particles9.2.1 Atomic Shell Structure and the Periodic Table of the Elements 9.3 Interacting Identical Particles9.3.1 Variational Principle9.3.2 Electrons in Atoms and Molecules10 Quantum Statistical Mechanics 10.1 Quantum Statistical Ensembles 1

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