8. Quantum Field Theory and Quantum Mechanics

• 8.1. Introduction
• 8.2. Standard Model
  • 8.2.1. Electroweak Standard Model
  • 8.2.2. QFT
  • 8.2.3. Low energy theories
• 8.3. Quantum Electrodynamics (QED)
  • 8.3.1. Local Gauge Invariance
  • 8.3.2. QED Lagrangian
  • 8.3.3. Magnetic moment of an electron
• 8.4. Quantum Mechanics
  • 8.4.1. From QED to Quantum Mechanics
  • 8.4.2. Perturbation Theory
  • 8.4.3. Scattering Theory
• 8.5. Systematic Perturbation Theory in QM
• 8.6. Appendix
  • 8.6.1. Units and Dimensional Analysis
  • 8.6.2. Atomic Units
  • 8.6.3. Tensors in Special Relativity and QFT
  • 8.6.4. Adding Angular Momenta
• 8.7. Examples
  • 8.7.1. Two Particles in Harmonic Potential
  • 8.7.2. Quantum Harmonic Oscillator
  • 8.7.3. Radial Schrödinger Equation
• 8.8. Radial Schrödinger and Dirac Equations
  • 8.8.1. Variational Formulation of the Schrödinger equation
  • 8.8.2. Radial Schrödinger equation
  • 8.8.3. Variational Formulation of the Dirac equation
  • 8.8.4. Radial Dirac equation
  • 8.8.5. Other Forms of Dirac Equations
  • 8.8.6. Asymptotic
• 8.9. Density Functional Theory (DFT)
  • 8.9.1. Many Body Schrödinger Equation
  • 8.9.2. The Hohenberg-Kohn Theorem
  • 8.9.3. The Kohn-Sham Equations
  • 8.9.4. The XC Term
  • 8.9.5. Total Energy
  • 8.9.6. XC Approximations
  • 8.9.7. Radial DFT Problem
  • 8.9.8. DFT As a Nonlinear Problem
  • 8.9.9. Thomas-Fermi-Dirac Theory
  • 8.9.10. Orbital Free Density Functional Theory
  • 8.9.11. References
• 8.10. Ideal Fermi Gas
  • 8.10.1. Low Temperature Limit
  • 8.10.2. High Temperature Limit
• 8.11. Hartree-Fock (HF) Method
  • 8.11.1. Derivation
  • 8.11.2. Roothaan Equations For Closed Shell Systems
  • 8.11.3. Two Particle Matrix Element
  • 8.11.4. General Matrix Elements in Spherical Symmetry
  • 8.11.5. Slater Type Orbitals (STO)
  • 8.11.6. Gaussian Type Orbitals (GTO)
  • 8.11.7. Exchange Integral in Spherical Symmetry
  • 8.11.8. Occupation Numbers
  • 8.11.9. Hartree Screening Functions
  • 8.11.10. Hartree Potential in Spherical Symmetry
  • 8.11.11. Nonlocal Exchange Potential in Spherical Symmetry
  • 8.11.12. Radial Hartree-Fock Equations
  • 8.11.13. Total Energy
  • 8.11.14. FEM
  • 8.11.15. 4-Index Transformation
  • 8.11.16. Green’s Functions
• 8.12. Projector Augmented-Wave Method (PAW)
  • 8.12.1. Projectors, Augmentation Spheres and Smooth Wavefunctions
  • 8.12.2. Frozen Core Approximation
  • 8.12.3. Expectation Values of Local Operators
  • 8.12.4. Kohn Sham Equations