MA4MP: Mathematical Physics

Module code: MA4MP

Module provider: Mathematics and Statistics; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: Level 4 (Undergraduate Masters)

When you'll be taught: Semester 1

Module convenor: Dr Patrick Ilg, email: p.ilg@reading.ac.uk

Module co-convenor: Dr Zuowei Wang, email: zuowei.wang@reading.ac.uk

Pre-requisite module(s): BEFORE TAKING THIS MODULE YOU MUST TAKE MA2MOD OR TAKE MA2MPH OR TAKE MT24B OR TAKE MT2AP (Compulsory)

Co-requisite module(s):

Pre-requisite or Co-requisite module(s):

Module(s) excluded: IN TAKING THIS MODULE YOU CANNOT TAKE MA3MP OR TAKE MA3SMA (Compulsory)

Placement information: NA

Academic year: 2024/5

Available to visiting students: Yes

Talis reading list: Yes

Last updated: 21 May 2024

Overview

Module aims and purpose

The module introduces students to core topics of mathematical physics, in particular Hamiltonian formulation of classical mechanics, quantum mechanics, and statistical mechanics.

Module learning outcomes

By the end of the module, it is expected that students will be able to:

1. Work competently with abstract theories of Mathematical Physics;
2. Use Hamiltonian’s formulation to critically analyse general properties of mechanical systems with some rigor and to solve corresponding model problems;
3. Systematically understand the theory of Quantum Mechanics and to investigate basic physical systems;
4. Use concepts of Statistical Mechanics, including entropy, ensembles, partition function and free energy to formulate and solve problems related to the equilibrium properties of physical systems.

Module content

Classical Mechanics will be formulated within a Hamiltonian framework. Besides elucidating the underlying mathematical structure of classical mechanics and the relation between symmetries and conservation laws, this framework serves us as a bridge to introduce Quantum Mechanics. Using an axiomatic approach, we will discuss several surprising properties of quantum systems, such as superposition principle and entanglement effects. A number of applications of Quantum Mechanics to relatively simple systems will be studied, including particles in potential wells, H-atoms, tunnelling, and first steps towards quantum information and computing.  

In the third part of this module, we will consider Hamiltonian systems consisting of many particles. We will introduce Statistical Mechanics as a theory to study the macroscopic equilibrium properties of such systems consisting of many constituents (atoms, particles, spins, etc.) under rather general conditions. The module will cover in a self-contained manner basic concepts in Statistical Mechanics, such as entropy, free energy, ensembles and partition functions, as well as their mathematical formulation. Applications to several model systems such as ideal and real gases and magnetic systems will serve to illustrate these concepts.

Structure

Teaching and learning methods

Lectures supported by problem sheets and tutorials. 

Study hours

At least 55 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.

Please note the independent study hours above are notional numbers of hours; each student will approach studying in different ways. We would advise you to reflect on your learning and the number of hours you are allocating to these tasks.

Semester 1 The hours in this column may include hours during the Christmas holiday period.

Semester 2 The hours in this column may include hours during the Easter holiday period.

Summer The hours in this column will take place during the summer holidays and may be at the start and/or end of the module.

Assessment

Requirements for a pass

Students need to achieve an overall module mark of 50% to pass this module.

Summative assessment

Penalties for late submission of summative assessment

The Support Centres will apply the following penalties for work submitted late:

Assessments with numerical marks

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of three working days;
• the mark awarded due to the imposition of the penalty shall not fall below the threshold pass mark, namely 40% in the case of modules at Levels 4-6 (i.e. undergraduate modules for Parts 1-3) and 50% in the case of Level 7 modules offered as part of an Integrated Masters or taught postgraduate degree programme;
• where the piece of work is awarded a mark below the threshold pass mark prior to any penalty being imposed, and is submitted up to three working days after the original deadline (or any formally agreed extension to the deadline), no penalty shall be imposed;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

Assessments marked Pass/Fail

• where the piece of work is submitted within three working days of the deadline (or any formally agreed extension of the deadline): no penalty will be applied;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension of the deadline): a grade of Fail will be awarded.

The University policy statement on penalties for late submission can be found at: /cqsd/-/media/project/functions/cqsd/documents/qap/penaltiesforlatesubmission.pdf

You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Formative assessment

Formative assessment is any task or activity which creates feedback (or feedforward) for you about your learning, but which does not contribute towards your overall module mark.

A number of selected problems from tutorial problem sheets. 

Reassessment

Additional costs