Course overview
This course will introduce Dirac's bra-ket formulation of quantum mechanics and make students familiar with various approximation methods applied to atomic, nuclear and solid-state physics, and to scattering. Content will include: Dirac's formulation of quantum mechanics: kets and bras, quantum oscillator, angular momentum, measurement, Bell's inequality, generalised Uncertainty Principle, connection with wave and matrix mechanics. Time-independent and time-dependent perturbation theory, Schrodinger, Heisenberg and Interaction pictures, radiative transitions. Identical particles, atoms, exchange forces, periodic systems, energy bands in solids. Symmetries, translations in space and time, parity and time reversal, rotations and angular momentum, addition of angular momenta, fine structure of Hydrogen, L-S and j-j coupling in atoms and nuclei. Hartree-Fock and Thomas-Fermi approximations, variational and WKB methods. Scattering: Born approximation, S-matrix, partial waves.
Course learning outcomes
- develop a knowledge and understanding of the concept that quantum states live in a vector space
- develop a knowledge and understanding of the meaning of measurement
- elate this abstract formulation to wave and matrix mechanics
- develop a knowledge and understanding of perturbation theory, level splitting, and radiative transitions
- develop a knowledge and understanding of the relation between conservation laws and symmetries
- develop a knowledge and understanding of the role of angular momentum in atomic and nuclear physics
- develop a knowledge and understanding of the scattering matrix and partial wave analysis
- solve quantum mechanics problems
- use the tools, methodologies, language and conventions of physics to test and communicate ideas and explanations