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MMath&Phys Mathematics and Physics / Course details
Year of entry: 2022
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Course unit details:
Mathematical Fundamentals of Quantum Mechanics
|Unit level||Level 3|
|Teaching period(s)||Semester 1|
|Available as a free choice unit?||No|
Mathematical Fundamentals of Quantum Mechanics (M)
|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.
To develop an understanding of quantum mechanics and in particular the mathematical structures underpinning it.
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.
- 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
Addition of angular momentum
- Approximate methods I: variational method and WKB (3 lectures)
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)
Feedback will be available on students’ solutions to examples sheets through examples classes, and model answers will be issued.
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)
|Scheduled activity hours|
|Assessment written exam||1.5|
|Independent study hours|
|Michael Birse||Unit coordinator|