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Accessibility statement
Qualification dates
StartEnd
03 Oct 2026Jun 2027
Our universe is full of matter, but the laws needed to explain this matter are complicated. In this module, you’ll learn some advanced tools from quantum and statistical mechanics, and use them to unveil the properties and behaviour of atoms, molecules and exotic states of matter. You’ll learn to navigate complex problems using approximations to the physics of many-electron systems, such as atoms and molecules and their interactions with electromagnetic fields. You’ll also discover how statistical mechanics can describe exotic matter, such as Bose–Einstein condensates and the complex interactions leading to magnetic materials.
This module comprises three parts.
Parts one and two are based on Physics of Atoms and Molecules by Bransden and Joachain. Part three is based on Topics in Statistical Mechanics by Cowan. Notes and video lectures guide you through the material in the books. There will also be tutorials to guide you through problem-solving.
Part 1
The first part covers the application of quantum mechanics to the interaction of hydrogen with electromagnetic fields. It begins with a review of quantum mechanical fundamentals and continues to describe the interactions between electromagnetic radiation and atoms by applying time-dependent perturbation theory. It discusses the origins of fine and hyperfine structure as perturbations representing relativistic effects and interactions of electrons with atomic nuclei. Using degenerate perturbation theory, you'll study interactions between atoms and static electric and magnetic fields.
Part 2
The second part examines the application of quantum mechanics to the complex many-electron systems of atoms and molecules. Topics in many-electron atoms include the central-field approximation and the periodic table, spin-orbit coupling and spectroscopy. It then discusses the quantum mechanics of many-electron states in molecules. We also expect to cover the electronic structure of diatomic molecules, the quantum mechanics associated with the rotation and vibration of diatomic molecules, and their molecular spectra.
Part 3
The final part introduces the statistical mechanics of matter. A review of thermodynamics and statistical mechanics includes an overview of canonical ensembles. The statistical mechanics of Bose and Fermi gases (i.e. quantum gases) follows. You’ll study metals and ultracold gases, leading to a discussion of Bose–Einstein condensation. The module finishes with a discussion of critical behaviour, where interactions lead to phase transitions. You’ll also study van der Waals gases and spin systems, with the phenomenological theory of phase transitions applied to magnetic materials and other systems.
This module contains advanced quantum mechanics. We strongly recommend you study degree-level quantum physics before studying this module.
You may not study this module on its own or as part of any qualification other than those listed below.
If you’re studying this module as part of our Master of Physics (M06), you must have completed all your Stage 3 modules (minimum Grade 3 passes recommended).
If you’re studying this module as part of our MSc in Mathematics (F04) or Postgraduate Diploma in Mathematics (E23), you must have passed Calculus of variations and advanced calculus (M820) or Analytic number theory I (M823). Additionally, before attempting this module, you should have studied at least one applied mathematics module.
If you’re studying this module as part of our MSc in Space Science and Technology (F77) or Postgraduate Diploma in Space Science and Technology (E90) or our Open Masters (F81), you must have a 2:2 (or higher) UK honours degree (or equivalent) in a related subject, i.e:
Are you ready for SM880?
You’ll get help and support from an assigned tutor throughout your module.
They’ll help by:
Online tutorials run throughout the module. While they’re not compulsory, we strongly encourage you to participate. Where possible, we’ll make recordings available.
Course work includes:
The first and last TMAs, plus the examination, assess Parts 1 and 3. The second TMA assesses Part 2.
For this module, we may use an assessment verification process to meet the requirements of relevant accrediting, professional, statutory or regulatory bodies. As part of this process, you may be asked to attend a short post-assessment video discussion, lasting around 15 minutes. During the discussion, you’ll need to show a photo ID and talk through your answers to a small number of questions with a tutor or a member of the module team. The discussion is not graded and is only used to confirm that you completed the assessment yourself.
We regularly review the assessments in our modules, so we may update the examination method used for this module to an in-person exam or a remotely invigilated (proctored) exam. When we are making such a change, we will make it clear on this page. If we need to make a change after you have registered, we will notify you as soon as possible. If you have additional requirements, we will support you to complete your assessments.
You’ll have access to a module website, which includes:
We’ll provide the electronic textbook Topics In Statistical Mechanics by Cowan. You’ll need to buy a copy of Physics of Atoms and Molecules by Bransden and Joachain.
The material contains small print and diagrams, which may cause problems if you have trouble reading text. If necessary, we’ll provide an electronic copy of Bransden and Joachain's Physics of Atoms and Molecules via the RNIB.
To find out more about what kind of support and adjustments might be available, contact us or visit our disability support pages.
Quantum and statistical mechanics of matter (SM880) starts once a year – in October.
It will next start in October 2026.
We expect it to start for the last time in October 2031.
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