Master of Mathematics and Physics (MMath&Phys)

MMath&Phys Mathematics and Physics

A diverse, varied course where you can draw on the combined expertise of three centres of University excellence.
  • Duration: 4 years
  • Year of entry: 2027
  • UCAS course code: FG3C / Institution code: M20
  • Key features:
  • Study abroad
  • Scholarships available
  • Accredited course

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Course unit details:
Statistical Mechanics

Course unit fact file
Unit code PHYS20352
Credit rating 10
Unit level Level 2
Teaching period(s) Semester 2
Offered by Department of Physics & Astronomy
Available as a free choice unit? No

Overview

Statistical Mechanics

Pre/co-requisites

Unit title Unit code Requirement type Description
Introduction to Quantum Mechanics PHYS20101 Pre-Requisite Compulsory
Properties of Matter PHYS20151 Pre-Requisite Compulsory

Aims

• To develop the statistical basis of classical thermodynamics

• To deepen the appreciation of the link between the microscopic properties of individual atoms or other particles and the macroscopic properties of many-body systems formed from them
 
• To demonstrate the power of statistical methods in different areas of physics
 
• To use the methods of quantum mechanics and statistical physics to calculate the behaviour of gases of identical particles, and to apply the results to a set of important physical system.

Learning outcomes

On completion successful students will be able to:
 
1. Explain the basic concepts of statistical mechanics, including entropy, its statistical interpretation and relation to disorder, and the statistical origin of the second law of thermodynamics;
 
2. Construct the canonical and grand-canonical partition functions for systems in thermal equilibrium, and use them to obtain thermodynamic quantities of interest.
 
3. Demonstrate an understanding of the implications of the indistinguishability of particles for systems of non-interacting quantum particles
 
4. Write down the Bose-Einstein and Fermi-Dirac distribution functions, and apply them to calculate the properties of Bose and Fermi gases, for example in the context of White Dwarf stars and black-body radiation.
 
5. Explain the physical origin of Bose-Einstein condensation, to characterize it quantitatively, and to explain the experiments confirming Bose-Einstein condensation

Syllabus

1.The statistical theory of thermodynamics (approximately 5 lectures)
 
Basic of probability theory; microstates and macrostates; the concept of ensembles; the statistical interpretation of entropy and temperature; isolated systems and the microcanonical ensemble
 
2. Statistical physics of non-isolated systems (approximately 8 lectures)
 
Derivation of the Boltzmann distribution and the canonical ensemble; the independent-particle approximation; the partition function and its connection with thermodynamics; examples of non-interacting systems (paramagnet set of harmonic oscillators – quantum and classical , ideal gas, classical and quantum rotors). Equipartition theorem; Density of states. Grand-canonical ensemble and chemical potential.
 
3. Quantum gases (approximately 10 lectures)
 
Fermi-Dirac and Bose-Einstein distributions. The ideal Fermi gas: Fermi energy. Electronic heat capacity. White Dwarf stars. The ideal Bose gas: Photon gas blackbody radiation (Stefan’s Law and the Planck formula). Bose-Einstein condensation.

Teaching and learning methods

CUIP Teaching Methods

Tutorials4
Lectures24


 

Assessment methods

Method Weight
Other 10%
Written exam 90%

* Other 10% Tutorial Work/attendance 

Feedback methods

Feedback is through weekly tutorials and marked tutorial work.

Recommended reading

Mandl, F., Statistical Physics, 2nd edition (Wiley) 

Bowley, R. & Sanchez, M. Introductory Statistical Mechanics, 2nd edition (Oxford)

Zemansky, M.W. & Dittman, R.H., Heat and Thermodynamics, 7th edition (McGraw Hill)

Steane, A.M., A complete undergraduate course Thermodynamics (Oxford University Press)

Blundell, S.J.  Blundell, K.M. Concepts in Thermal Physics (Oxford University Press)

 

Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 24
Tutorials 4
Independent study hours
Independent study 70.5

Teaching staff

Staff member Role
Judith McGovern Unit coordinator

Fees and funding

Fees

Tuition fees for home students will be £10,050 for the 2027/28 academic year. In England and Wales, tuition fees for home undergraduate students are subject to the Government fee cap, which the Government has announced will be £10,050 for the 2027/28 academic year.

Government policy is to increase the fee cap on an annual basis to reflect inflation (i.e. increasing costs), and the tuition fee home students pay in subsequent academic years will reflect any increases in the Government fee cap (which we will communicate to you as soon as we can in advance of the relevant academic year).

For general information please see the undergraduate finance pages.

Policy on additional costs

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

Scholarships/sponsorships

The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability and we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.

For information about scholarships and bursaries please visit our undergraduate student finance pages and our Department funding pages .

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