Undergraduate Course: Quantum Mechanics (PHYS09053)
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 | 20 |
ECTS Credits | 10 |
| Summary | This two-semestered course covers fundamentals of quantum mechanics and its applications to atomic and molecular systems.
The first semester covers non-relativistic quantum mechanics, supplying the basic concepts and tools needed to understand the physics of atoms, molecules, and the solid state. 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.
The second semester deals principally with atomic structure, the interaction between atoms and fields, and the atom-atom interactions in molecular physics, via a variety of approximation method. The course presents 1st and 2nd order non-degenerate perturbation theory, as well as 1st order degenerate perturbation theory, with a strong focus on problem-solving. This is then complemented by the Rayleigh-Ritz variational approach. Multi-electron atoms are discussed and, finally, molecular bonds and the LCAO method are introduced.¿
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| Course description |
This is a core course in quantum mechanics, delivering the following content across two semesters.
Semester 1:
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.
Semester 2:
1. Non-degenerate perturbation theory. Applications to include particles in a square well, simple-harmonic oscillator or Coulomb potential, subject to perturbations deriving from an externally applied field.
2. Degenerate perturbation theory. Applications to include excited states of the hydrogen atom and the square well or harmonic oscillator in more than one dimension.
3. Combining two degrees of freedom, including spin. To include combinations of different angular momentum states (with application to the fine structure of hydrogen) and symmetry requirements on quantum states of fermions and bosons.
4. Atoms with more than one electron. To include ground and excited states of helium-like atoms, treated using perturbation theory applied to the hydrogen atom and the variational method. To include also ground states of many-electron atoms via the Aufbau principle and Hund¿s rules.
5. Formation and dynamics of molecular bonds. Schematic treatment of molecules using linear combinations of atomic orbitals / molecular orbitals. Consideration of slow degrees of freedom (rotations and vibrations) arising from the effective interaction between nuclei mediated by electrons.
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Information for Visiting Students
| Pre-requisites | Students are expected to be fluent in linear algebra methods and concepts, and in one- and several-variable calculus (as described in PHYS08042 Linear Algebra and Several Variable Calculus and PHYS08043 Dynamics and Vector Calculus). |
| High Demand Course? |
Yes |
Course Delivery Information
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| Academic year 2026/27, Available to all students (SV1)
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Quota: None |
| Course Start |
Full Year |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Lecture Hours 44,
Seminar/Tutorial Hours 44,
Formative Assessment Hours 3,
Revision Session Hours 1,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
104 )
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| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
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| Additional Information (Assessment) |
Coursework 20%
Examination 80% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Minutes |
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| Main Exam Diet S2 (April/May) | Quantum Mechanics May Exam Diet | 180 | |
Learning Outcomes
On completion of this course, the student will be able to:
- 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 quan- tum mechanics by breaking it down into its constituent parts
- Apply the necessary 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
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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)
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Special Arrangements |
None |
| Keywords | QMech |
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 |
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