Advanced Quantum Physics

Wedi cwblhau'r modiwl dylai'r myfyrwyr fedru:

1. Display mastery of the fundamental postulates of Quantum Mechanics.
2. Formulate and evaluate simple model potential systems for elementary phenomena such as tunnelling and scattering and the hydrogen atom.
3. Demonstrate the variational method for approximating the ground state of quantum mechanical systems.
4. Describe and derive both time-independent and time-dependent perturbation theory.
5. Formulate the description of open quantum systems, master equations, and evaluate and discuss their predictions for specific models.

Quantum mechanics is increasingly more important to technology. With the techniques of quantum chemistry the properties can be predicted for larger and larger molecules, leading to applications e.g. in drug design. Quantum mechanics is also leading to new technologies in a more direct way, e.g. through quantum computing.
This module introduces some of the theory behind these advanced applications. It introduces variational theory and perturbation theory, which underpin modern quantum chemistry. Furthermore, operator theoretic concepts are introduced with the aim of describing open quantum systems.

This MPhys module builds on PH23010 Principles of Quantum Mechanics. The fundamentals and basic results of quantum mechanics are re-capped with a higher level of rigour. New topics are introduced such as perturbation theory (both time-dependent and time-independent) and quantum optics with applications to modern quantum technologies.

1. Fundamentals of quantum mechanics and their relation to the properties of operators, wavefunctions and the eigenvalues that are observed.
2. Model potential well systems: finite potential well, scattering and tunneling, cubic and spherical wells.
3. Variational method.
4. Perturbation theory: stationary theory (non-degenerate: 1st and 2nd order, degenerate: 1st order), time-dependent: oscillating perturbation, radiative transition.
5. Evolution of a system and environment, reduced dynamics, the master equation, complete positivity and quantum information channels, Lindblad generators.

Mae'r modiwl hwn yn cydymffurfio a FfCChC Lefel 7