1 Relativistic Theory and Electron Spin
1.1 Dirac Equation
1.1.1 Attempts for a Relativistic Theory
1.1.2 Physics Implied in Dirac Equation
1.1.3 Massless Dirac Particles
1.2 Scattering by Step Potential and Klein Parado
1.3 Non—relativistic Limit
1.3.1 Pauli Equation.
1.3.2 Spin—orbit Coupling
1.4 Spin—orbit Coupling in Solid Materials
1.4.1 Rashba Spin—orbit Coupling
1.4.2 Spin Current and Spin—related Force
2 Density Matrix and Quantum Coherence
2.1 Pure and Mixed Spin States
2.2 The Density Matrix
2.3 Quantum Coherence
2.3.1 Quantum Beat
2.3.2 Double—slit Interference
2.4 Time Evolution of Mixed States
2.4.1 Liouville Equation
2.4.2 Reduced Density Matrix
3 Utilizing Quantum States
3.1 Schmidt Decomposition
3.2 Entangled States
3.3 Von Neumann Measurement and EPR Paradox
3.4 Quantum Teleportation
3.5 Some Concepts for Quantum Computation
4 Phase Playing a Role
4.1 Aharonov—Bohm Effect
4.2 Motion in Periodic Potentials and Band Structure
4.2.1 Bloch Theorem and Band Structure
4.2.2 Some Simple Examples
4.3 Adiabatic Theorem
4.4 Berry Phase
5 Approximation Methods
5.1 Variational Approach
5.1.1 The Variational Principle
5.1.2 Ground State of Helium Atom
5.2 Born—Oppenheimer Approximation
5.2.1 Hydrogen Molecular Ion
5.2.2 Hydrogen Molecule
5.3 Mean Field Approach
5.3.1 Hartree Self-consistent—field Approach
5.3.2 Hartree—Fock Approach
5.4 Other Approximations
5.4.1 Thomas—Fermi Approximation
5.4.2 The WKB Approximation
Index
