QM11 · Relativistic & advanced
A 34-module path through qm11 · relativistic & advanced, in study order from foundations to the frontier.
Modules
- The Klein-Gordon Equation
- Klein-Gordon Probability Current and Negative Densities
- Negative-Energy Solutions and the Interpretive Crisis
- The Dirac Equation
- Dirac Gamma Matrices and Clifford Algebra
- Dirac Spinors and Plane-Wave Solutions
- Lorentz Covariance of the Dirac Equation
- Bilinear Covariants and Dirac Adjoint
- Spin from the Dirac Equation
- The Dirac Sea and Antiparticles
- Charge Conjugation and the Positron
- Nonrelativistic Reduction and the Pauli Equation
- Foldy-Wouthuysen Transformation
- Relativistic Corrections to the Hydrogen Atom
- Spin-Orbit Coupling from Relativity
- The Darwin Term and Zitterbewegung
- Exact Dirac Solution of the Hydrogen Atom
- The Klein Paradox
- The Feynman Path Integral Formulation
- The Propagator from Path Integrals
- Free-Particle and Harmonic-Oscillator Path Integrals
- Path Integral and the Schrödinger Equation
- Imaginary-Time and Euclidean Path Integrals
- Instantons and Quantum Tunneling
- The WKB Approximation (QM11)
- Connection Formulas and Turning Points
- Bohr-Sommerfeld and Maslov Quantization
- Stationary Phase and the Classical Limit
- The Aharonov-Bohm Effect via Path Integrals
- Second Quantization and Fock Space
- From Single-Particle to Quantum Fields
- Field Quantization of the Klein-Gordon and Dirac Fields
- The Feynman Propagator and Causality
- Spin-Statistics and the CPT Theorem