Advanced Quantum Theory
| Code | School | Level | Credits | Semesters |
| MATH3010 | Mathematical Sciences | 3 | 20 | Autumn UK |
- Code
- MATH3010
- School
- Mathematical Sciences
- Level
- 3
- Credits
- 20
- Semesters
- Autumn UK
Summary
This course builds on the foundations of quantum mechanics introduced in the module MATH2013. It further develops the fundamental theory so that it applies to more general problems, such as those involving spin, and introduces key calculational approaches, such as those underlying angular momentum, the hydrogen atom, scattering problems and approximation methods such as perturbation theory.
The module begins with a description of the quantum theory of angular momentum, using ladder operators and introducing the concept of spin. The quantum theory of the Hydrogen atom is then described, incorporating aspects of angular momentum such as spin. The fundamental formalism of quantum mechanics is set out in a more general setting than considered in MATH2013, introducing concepts such as bra-ket notation, symmetries, unitary operators and the Heisenberg picture. Approximation methods such as perturbation theory and variational approaches are described and scattering theory is introduced in the context of three-dimensional wave propagation in a central potential.
Target Students
Single and Joint Honours students from the School of Mathematical Sciences. Mathematical Physics and Natural Sciences students.
Classes
- Two 1-hour lectures each week for 11 weeks
- One 2-hour lecture each week for 11 weeks
Assessment
- 100% Exam 1 (3-hour): Written examination
Assessed by end of autumn semester
Educational Aims
Thiscourse provides a foundation in the key ideas of the formalism of quantum mechanics and the main calculational approaches to it, building on the more elementary description introduced in thecourse MATH2013. The formalism is developed so that it applies to general nonrelativistic problems and so that it provides a basis for future development in the relativistic setting. Thecourse also develops essential methods of calculation in quantum mechanics, such as those underlying angular momentum and the Hydrogen atom, approaches exploiting bra-ket notation, and the key ideas underpinning approximation methods and scattering theory.Learning Outcomes
A student who completes this course successfully will be able to:
L1 - apply the theory underlying angular momentum and spin;
L2 - use methods and derive results of the theory of the Hydrogen atom;
L3 - derive results and solve problems relevant to the fundamental formalism of quantum mechanics;
L4 - obtain solutions to problems in quantum mechanics using approximation methods;
L5 - apply the theory of quantum scattering of particles in a spherically symmetric potential.