Quantum Mechanics

1. Quantum Mechanics Applications
   1. Quantum Computing
      1. Qubits and Quantum Gates
         1. Definition and properties of qubits
         2. Basic quantum gates: Pauli-X, Pauli-Y, Pauli-Z
         3. Multi-qubit gates: CNOT, Toffoli
         4. Universal quantum gate sets
      2. Quantum Algorithms
         1. Shor's Algorithm
            1. Prime factorization process
            2. Quantum Fourier transform
            3. Implications for modern cryptography
         2. Grover's Algorithm
            1. Quantum search efficiency
            2. Oracle-based queries
      3. Quantum Error Correction
         1. Error sources: decoherence and operational errors
         2. Quantum error-correcting codes: Shor code, Steane code
         3. Fault-tolerant quantum computation
   2. Quantum Cryptography
      1. Quantum Key Distribution (QKD)
         1. Basic principles and protocols: BB84, E91
         2. Entanglement-based QKD
      2. Quantum Security
         1. Security leveraging quantum mechanics features
         2. Eavesdropping detection
         3. Challenges and current advancements
   3. Quantum Optics
      1. Photons and Light-Matter Interaction
         1. Quantum nature of light and photon statistics
         2. Quantum description of light-matter interaction
      2. Laser Physics
         1. Coherence properties
         2. Quantum theory of laser operation
         3. Applications in precision measurements
   4. Quantum Chemistry
      1. Molecular Orbitals
         1. Quantum mechanical treatment of molecules
         2. Hybridization of atomic orbitals
         3. Modern computational methods
      2. Quantum Chemical Calculations
         1. Hartree-Fock approximation
         2. Post-Hartree-Fock methods: CI, MP2
         3. Density functional theory (DFT) and its applications
   5. Quantum Field Theory
      1. Quantum Electrodynamics (QED)
         1. Interaction of light and matter
         2. Feynman diagrams and path integrals
         3. Renormalization and its significance
      2. Quantum Chromodynamics (QCD)
         1. Fundamental forces and particle interactions
         2. Quarks, gluons, and confinement
         3. Lattice QCD techniques and simulations