Quantum Field Theory and Quantum Mechanics

• Introduction
• Standard Model
  • Electroweak Standard Model
  • QFT
  • Low energy theories
• Quantum Electrodynamics (QED)
  • QED Lagrangian
  • Magnetic moment of an electron
• Quantum Mechanics
  • From QED to Quantum Mechanics
  • Perturbation Theory
  • Scattering Theory
• Systematic Perturbation Theory in QM
• Appendix
  • Units and Dimensional Analysis
  • Atomic Units
  • Tensors in Special Relativity and QFT
  • Adding Angular Momenta
• Examples
  • Two Particles in Harmonic Potential
  • Quantum Harmonic Oscillator
  • Radial Schrödinger Equation
• Radial Schrödinger and Dirac Equations
  • Variational Formulation of the Schrödinger equation
  • Radial Schrödinger equation
  • Variational Formulation of the Dirac equation
  • Radial Dirac equation
  • Other Forms of Dirac Equations
• Density Functional Theory (DFT)
  • Many Body Schrödinger Equation
  • The Hohenberg-Kohn Theorem
  • The Kohn-Sham Equations
  • The XC Term
  • Total Energy
  • XC Approximations
  • Radial DFT Problem
  • DFT As a Nonlinear Problem
  • References
• Hartree-Fock (HF) Method
  • Derivation
  • Roothaan Equations For Closed Shell Systems
  • Two Particle Matrix Element
  • General Matrix Elements in Spherical Symmetry
  • Slater Type Orbitals (STO)
  • Exchange Integral in Spherical Symmetry
  • Occupation Numbers
  • Hartree Screening Functions
  • Hartree Potential in Spherical Symmetry
  • Nonlocal Exchange Potential in Spherical Symmetry
  • Radial Hartree-Fock Equations
  • Total Energy
  • FEM
  • 4-Index Transformation
  • Green’s Functions
• Projector Augmented-Wave Method (PAW)
  • Projectors, Augmentation Spheres and Smooth Wavefunctions
  • Frozen Core Approximation
  • Expectation Values of Local Operators
  • Kohn Sham Equations