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.
What you will study
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.
You will learn
The main aim of this module is to develop your advanced understanding of physics and expand your reasoning and problem-solving through the teaching of quantum and statistical mechanics.
Entry
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:
- BSc with applied mathematics content, e.g: Mathematics, Applied Mathematics, Mathematics with Applied Mathematics.
- BSc with “physics” in the title, e.g: Astrophysics, Chemical Physics, Computational Physics, Mathematical Physics, Mathematics and Physics, Physics, Physics with Astronomy, Physics with Theoretical Physics, Theoretical Physics.
Are you ready for SM880?
If English isn’t your first language, we recommend you have a minimum IELTS (International English Language Testing System) score of 7.
Teaching and assessment
Support from your tutor
Throughout your module studies, you’ll get help and support from your assigned module tutor. They’ll help you by:
- marking your assignments (TMAs) and providing detailed feedback for you to improve
- providing individual guidance, whether for general study skills, specific module content or additional learning resources.
The module has a dedicated and moderated forum where you can join in online discussions with your fellow students. There are also online tutorials. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part.
Assessment
The assessment details can be found in the facts box.
The first and last TMAs plus the examination assess Parts 1 and 3. The second TMA assesses Part 2.
Future availability
Quantum and statistical mechanics of matter (SM880) starts once a year – in October.
This page describes the module that will start in October 2026.
We expect it to start for the last time in October 2031.