This course marks the initial segment of a two semester quantum physics series at CCU.
1. Approximation methods for time-independent Hamiltonians
• Time-independent perturbation theory: non-degenerate and degenerate perturbations and the Start effect
• The real Hydrogen spectrum: relativistic mass correction, spin-orbital coupling, the Zeeman effect and the hyperfine splitting
• Semi-classical approximation (WKB)
• Variational approximation
2. Identical Particles and Quantum Statistical Mechanics
• Fermions and Bosons: N-particles system, exchange operator, symmetrization postulate, hydrogen molecule and helium atom
• Quantum statistical mechanics: the most probable configuration, three statistics and the black-body spectrum
• Degenerate Fermi gas: density of state, degeneracy pressure, white dwarf stars, Chandrasekhar limit and neutron star
• Electron in metals: periodic potential, Block waves, band structure, metal-insulator-semiconductor barrier
3. Charge particles ia magnetic field
• Canonical quantization
• The classical particle interacting with EM field
• Electron moving in a constant magnetic field
• The degeneracy of Landau levels
• Integer Quantum Hall effect
4. Time Dependent Perturbation Theory and Adiabatic Approximation
• Time-dependent perturbation
⁃ General formula
⁃ Harmonic time-varying of the potential
⁃ Life--time, line widths, and resonances
⁃ Phase space
• Radiation
⁃ Semiclassical treatment of the EM field
⁃ Quantization of the EM field
⁃ Matrix element and selection rules
⁃ 2p to1s transition
⁃ Spin and intensity rules
• The adiabatic and Born-Oppenheimer approximation (optional)
⁃ The Born-Oppenheimer approximation and the rotation/vibration of molecules
⁃ The adiabatic theorem
⁃ Berry's phase
⁃ The Aharonov-Born effect
5. Scattering and Identical particles
• Introduction
• partial wave expansion and phase shift
• The Born approximation
• Scattering of identical particles
• Inelastic scattering