Undergraduate Course: Foundations of Quantum Mechanics (PHYS09051)
Course Outline
| School | School of Physics and Astronomy |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 9 (Year 3 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | This course covers the fundamentals concepts and tools of non-relativistic quantum mechanics. It is not intended as the very first contact with quantum mechanics, although previous knowledge is not required.
After reviewing the need and the goals of a ¿good¿ quantum theory, we introduced the postulates and rules of Quantum Mechanics. Several important 1D and 3D problems are then presented and solved. We then introduce Dirac notation and an algebraic approach to Quantum Mechanics, deriving important results. The new methodology is used to revisit the Harmonic Oscillator and Angular Momentum, showing the emergence of integer and half-integer j. The semester finishes with the introduction of the spin-statistics theorem and addition of angular momentum, briefly showcasing entanglement. |
| Course description |
The course presents material in a similar form and detail to Griffiths or Brandsen & Joachain, covering the following topics.
0. Introduction. Necessity of a new theory. Stern-Gerlach experiment.
1. Wave mechanics. Postulates of Quantum Mechanics. Observables, measurement and probabilities. Time evolution of a state. Solving the Schrödinger equation for various 1D potentials: bound and unbound states, transmission and reflection coefficients. Parity as a symmetry operation. The Schrödinger equation in 3D: separation of variables, introduction to angular momentum, the hydrogen atom.
2. Dirac notation. Link between quantum mechanics, linear algebra and Fourier analysis. Completeness and orthogonality relations, including unbound states. Observables and operators. Hermitian and unitary operators. Time evolution. Commuting observables.
3. Matrix mechanics. Conserved quantities and Heisenberg¿s equation of motion. The uncertainty principle. Revisiting the harmonic oscillator: annihilation and creation operators. Revisiting angular momentum: ladder operators and the emergence of half-integer j. The Stern-Gerlach experiment as an idealised quantum system.
4. The spin-statistics theorem: introduction of identical particles. Stating, but not proving, the angular momentum addition theorem. Entangled states.
|
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
|
Co-requisites | |
| Prohibited Combinations | Students MUST NOT also be taking
Quantum Mechanics (PHYS09053)
|
Other requirements | None |
| Additional Costs | None |
Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2026/27, Part-year visiting students only (VV1)
|
Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Supervised Practical/Workshop/Studio Hours 20,
Summative Assessment Hours 2,
Revision Session Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
52 )
|
| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Exam 80% and coursework 20% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Minutes |
|
| Main Exam Diet S1 (December) | Foundations of Quantum Mechanics - December | 120 | | | Resit Exam Diet (August) | Foundations of Quantum Mechanics - August | 120 | |
Learning Outcomes
- State in precise terms the foundational principles of quantum mechanics and how they relate to broader physical principles.
- Devise and implement a systematic strategy for solving a complex problem in quantum mechanics by breaking it down into its constituent parts.
- Apply a wide range of mathematical techniques to build up the solution to a complex physical problem.
- Use experience and intuition gained from solving physics problems to predict the likely range of reasonable solutions to an unseen problem.
- Resolve conceptual and technical difficulties by locating and integrating relevant information from a diverse range of sources.
|
Reading List
D. J. Griffiths, ¿Introduction to Quantum Mechanics¿ (Pearson/Prentice-Hall, 2005)
J. J. Sakurai and J. Napolitano, ¿Modern Quantum Mechanics¿, 3rd ed. (Cambridge University Press, 2021) |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | FQMech |
Contacts
| Course organiser | Dr Miguel Martinez-Canales
Tel: (0131 6)51 7742
Email: miguel.martinez@ed.ac.uk |
Course secretary | Ms Nicole Ross
Tel:
Email: nicole.ross@ed.ac.uk |
|
|
University Homepage