Quantum mechanics introduces a dramatically new and rich understanding of the universe. In
addition to providing a much deeper insight into the world of atoms and subatomic particles than
afforded by classical Newtonian physics, quantum mechanics underpins advances in science across
all disciplines, from molecular biology to astrophysics.
This subject provides a rigorous mathematical
formalism for advanced quantum mechanics, laying the foundation for further fundamental theoretical
physics and research-level experimental physics in frontier areas such as quantum communication
and quantum computation.
The subject describes the Hilbert-space formulation of quantum wave mechanics, including density
matrix descriptions for single and joint Hilbert space systems; symmetries and conservation laws
including rotations and angular momentum; many-body systems of identical particles; time-dependent
perturbation theory, and scattering theory.
Subject objectives
The objectives of this subject are:
- Understanding the Hilbert-space formalism of modern quantum mechanics, with bra-ket and matrix
notations, and the role of symmetries and related conservation laws
- Understanding density matrices for single and joint Hilbert spaces, the difference between pure and
mixed states, and entanglement
- Understanding how many-body systems can be treated with a modern quantum mechanical
framework
- Ability to apply time-dependent perturbation methods to physical systems and thus predict
measurable outcomes
- Knowledge of representative applications including scattering