PHY3062 | 2023 | University of Exeter

MODULE TITLE	Methods of Theoretical Physics	CREDIT VALUE	15
MODULE CODE	PHY3062	MODULE CONVENER	Prof Mikhail (Misha) Portnoi (Coordinator)

DURATION: TERM	1	2	3
DURATION: WEEKS	11

Number of Students Taking Module (anticipated)	46

DESCRIPTION - summary of the module content

The mathematical techniques presented relate directly to the advanced modules at Stages 3 and 4 of Physics programmes, and also have wide applicability across the mathematical sciences. Practical skills are emphasised, rather than formal proofs.

AIMS - intentions of the module

This module aims to develop a deeper understanding of, and greater competence in using, some of the important mathematical methods and techniques of theoretical physics not covered in PHY2025.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

A student who has passed this module should be able to:

Module Specific Skills and Knowledge:

1. find a Laurent expansion of a function of a complex variable; identify poles and branch points;

2. evaluate a wide variety of definite integrals using the calculus of residues;

3. use symmetry arguments when evaluating integrals;

4. approximate the value of a definite integral using the method of steepest descent;

5. deduce the first term in Stirling's expansion of the factorial function;

6. approximate the value of the ground-state energy of a bound particle by using the variational method;

7. find approximate solutions of the Shrödinger equation using the WKB method;

8. identify the point group of a simple symmetric object;

9. identify the 'bond', 'site' and continuum problems of percolation theory;

10. solve problems using the theory of conformal mapping;

Discipline Specific Skills and Knowledge:

11. apply analytical and numerical skills in mathematics;

12. formulate problems in a logical manner;

13. adapt and apply the methods discussed in lectures to unseen problems;

Personal and Key Transferable / Employment Skills and Knowledge:

14. present and justify use of techniques and methods;

15. work in groups - students are encouraged to work co-operatively together to solve assigned problems.

SYLLABUS PLAN - summary of the structure and academic content of the module

I. Functions of a Complex Variable

Revision of basic notations and properties of complex numbers
Analytic functions
Cauchy's theorem
Laurent expansion
Calculus of residues

II. Evaluation of Integrals

Elementary methods
Use of symmetry
Contour integration

III. Conformal Mapping

Theory
Applications

IV. Approximate Methods

Method of steepest descent
The WKB method
Variational method in quantum mechanics

V. Special Chapters

Elements of group theory
Elements of percolation theory
Non-linear Shrödinger equation (an example)

LEARNING AND TEACHING

LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)

Scheduled Learning & Teaching Activities	22	Guided Independent Study	128	Placement / Study Abroad

DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS

Category	Hours of study time	Description
Scheduled learning & teaching activities	20 hours	20×1-hour lectures
Scheduled learning & teaching activities	2 hours	2×1-hour problems/revision classes
Guided independent study	30 hours	5×6-hour self-study packages
Guided independent study	16 hours	4×4-hour problem sets
Guided independent study	82 hours	Reading, private study and revision

ASSESSMENT

FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade

Form of Assessment	Size of Assessment (e.g. duration/length)	ILOs Assessed	Feedback Method
Guided self-study (0%)	5×6-hour packages (fortnightly)	1-14	Discussion in class
4 × Problems sets (0%)	4 hours per set (fortnightly)	1-14	Solutions discussed in problems classes.

SUMMATIVE ASSESSMENT (% of credit)

Coursework	0	Written Exams	100	Practical Exams

DETAILS OF SUMMATIVE ASSESSMENT

Form of Assessment	% of Credit	Size of Assessment (e.g. duration/length)	ILOs Assessed	Feedback Method
Final Examination	100%	2 hours 30 minutes (January)	1-13	Mark via MyExeter, collective feedback via ELE and solutions.

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)

Original Form of Assessment	Form of Re-assessment	ILOs Re-assessed	Time Scale for Re-assessment
Whole module	Written examination (100%)	1-13	August/September assessment period

Re-assessment is not available except when required by referral or deferral.

RE-ASSESSMENT NOTES

An original assessment that is based on both examination and coursework, tests, etc., is considered as a single element for the purpose of referral; i.e., the referred mark is based on the referred examination only, discounting all previous marks. In the event that the mark for a referred assessment is lower than that of the original assessment, the original higher mark will be retained.

Physics Modules with PHY Codes

Referred examinations will only be available in PHY3064, PHYM004 and those other modules for which the original assessment includes an examination component - this information is given in individual module descriptors.

RESOURCES

INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE:

http://newton.ex.ac.uk/redirects/ELE/phy3062

Reading list for this module:

Type	Author	Title	Edition	Publisher	Year	ISBN
Extended	Mathews J. and R. L. Walker	Mathematical Methods of Physics	2nd	Benjamin	1970	0-805-37002-1
Extended	Stauffer, D.	Introduction to Percolation Theory		Taylor and Francis	1985	0-850-663156

CREDIT VALUE	15	ECTS VALUE	7.5

PRE-REQUISITE MODULES	PHY2025
CO-REQUISITE MODULES

NQF LEVEL (FHEQ)	6	AVAILABLE AS DISTANCE LEARNING	No
ORIGIN DATE	Monday 6th December 2021	LAST REVISION DATE	Thursday 26th January 2023

KEY WORDS SEARCH	Physics; Method; Integrals; Functions; Theory; Expansion; Laurent; Variational; Calculus; Elements; Variable.

Methods of Theoretical Physics - 2023 entry