1 Basics
1.1 What has to be explained by Quantum mechanics?
1.2 Mathematical Basics
1.3 The linear Hermitian operator
1.4 Eigenvalues and Eigenvectors of matrices
1.5 Component representation of linear operators
2 Fundamentals of Quantum Mechanics
2.1 The Axioms of Quantum Mechanics
2.2 First Remarks
2.3 Calculation of expectation values
2.4 Operators representing physical properties
2.5 Measuring quantum mechanical properties
2.6 The Uncertainty relation
2.7 The Particle-Wave-Dualism
2.8 The Commutator
2.8.1 What is an electron
3 The description of a quantum mechanical system
3.1 The correspondence principle
3.2 Conserved Properties/Constants of Motion
3.3 Hybridization
3.4 Why do atoms radiate light?
3.5 Why does a quantum mechanical state change?
3.6 Many-particle theory
3.7 The Pauli principle
3.8 Orbital angular momentum and spin
4 The description of the electronic (ground-) state of a solid
4.1 The periodic, perfect solid
4.2 The Bloch-Theorem
4.3 Proof of the Bloch-Theorem
4.4 The Hamiltonian and its symmetry operations
4.5 The ”Tight-Binding”-Method: LCAO
4.6 General solution of LCAO
4.7 Applying the LCAO method to s-band electrons
4.8 The two atoms containing molecule
4.9 Magnetic properties of the two electron system: singlet and triplet state
4.9.1 Mean-Field-Approximation for the description of the Coulomb-Coupling
4.10 The covalent bond
5 The influence of temperature on many particle systems
5.1 One electron approximation
5.2 The thermodynamic equilibrium
5.3 The Fermi statistics
5.4 Ferromagnetism in ”mean-field” approximation