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- UCAS course code
- F345
- UCAS institution code
- M20
Course unit details:
Mathematical Fundamentals of Quantum Mechanics
Unit code | PHYS30201 |
---|---|
Credit rating | 10 |
Unit level | Level 3 |
Teaching period(s) | Semester 1 |
Available as a free choice unit? | No |
Overview
Mathematical Fundamentals of Quantum Mechanics (M)
Pre/co-requisites
Unit title | Unit code | Requirement type | Description |
---|---|---|---|
Linear Algebra B | MATH10212 | Pre-Requisite | Compulsory |
Introduction to Quantum Mechanics | PHYS20101 | Pre-Requisite | Compulsory |
Fundamentals of Solid State Physics | PHYS20252 | Pre-Requisite | Recommended |
Complex Variables and Vector Spaces | PHYS20672 | Pre-Requisite | Compulsory |
For recommneded theory units following this module please see PHYS40481 and 40682.
Aims
To develop an understanding of quantum mechanics and in particular the mathematical structures underpinning it.
Learning outcomes
On completion of the course, successful students should be able to:
1. Use Dirac notation to represent quantum-mechanical states and manipulate operators in terms of their matrix elements.
2. Solve a variety of problems with model and more realistic Hamiltonians, demonstrating an ability to use the mathematical underpinning of quantum mechanics.
3. Work with angular momentum operators and their eigenvalues both qualitatively and quantitatively.
4. Use perturbation theory and other methods to find approximate solutions to problems in quantum mechanics, including the fine-structure of energy levels of hydrogen.
Syllabus
- The Fundamentals of Quantum Mechanics (6 lectures)
Postulates of quantum mechanics
Time evolution: the Schrödinger equation and the time evolution operator
Ehrenfest’s theorem and the classical limit
The simple harmonic oscillator: creation and annihilation operators
Composite systems and entanglement
- Angular Momentum (7 lectures)
General properties of angular momentum
Electron spin and the Stern-Gerlach experiment
Higher spins
Addition of angular momentum
Vector Operators
- Approximate methods I: variational method and WKB (3 lectures)
Variational methods
WKB approximation for bound states and tunneling
- Approximate methods II: Time-independent perturbation theory (5 lectures)
Non-degenerate and degenerate perturbation theory
The fine structure of hydrogen
External fields: Zeeman and Stark effect in hydrogen
- The Einstein-Poldosky-Rosen “paradox” and Bell’s inequalities (1 lecture)
Assessment methods
Method | Weight |
---|---|
Written exam | 100% |
Feedback methods
Feedback will be available on students’ solutions to examples sheets through examples classes, and model answers will be issued.
Recommended reading
Shankar, R. Principles of Quantum Mechanics 2nd ed. (Plenum 1994)
Gasiorowicz, S. Quantum Physics, 3rd ed. (Wiley, 2003)
Mandl, F. Quantum Mechanics (Wiley, 1992)
Griffths, D. J. Introduction to Quantum Mechanics, 2nd ed (CUP, 2017)
Study hours
Scheduled activity hours | |
---|---|
Assessment written exam | 1.5 |
Lectures | 22 |
Independent study hours | |
---|---|
Independent study | 76.5 |
Teaching staff
Staff member | Role |
---|---|
Michael Birse | Unit coordinator |