Part IX: Advanced Topics
Modern quantum mechanics: path integrals, density matrix formalism, quantum entanglement, Bell's inequalities, decoherence, quantum information, and an introduction to relativistic quantum mechanics.
60+ pages | 7 chapters
1. Path Integral Formulation (12 pages)
Feynman path integrals, sum over histories, propagator
2. Density Matrix Formalism (8 pages)
Mixed states, pure states, von Neumann entropy, decoherence
3. Quantum Entanglement (10 pages)
EPR paradox, entangled states, non-locality, CHSH inequality
4. Bell's Inequalities (7 pages)
Local hidden variables, Bell's theorem, experimental tests
5. Decoherence (8 pages)
Environment-induced decoherence, pointer basis, quantum-to-classical transition
6. Quantum Information Basics (9 pages)
Qubits, quantum gates, no-cloning theorem, quantum teleportation
7. Relativistic QM & Dirac Equation (6 pages)
Klein-Gordon equation, Dirac equation, antiparticles, spin