Study information

# Methods of Theoretical Physics - 2023 entry

MODULE TITLE CREDIT VALUE Methods of Theoretical Physics 15 PHY3062 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
1. Revision of basic notations and properties of complex numbers
2. Analytic functions
3. Cauchy's theorem
4. Laurent expansion
5. Calculus of residues
II. Evaluation of Integrals
1. Elementary methods
2. Use of symmetry
3. Contour integration
III. Conformal Mapping
1. Theory
2. Applications
IV. Approximate Methods
1. Method of steepest descent
2. The WKB method
3. Variational method in quantum mechanics
V. Special Chapters
1. Elements of group theory
2. Elements of percolation theory
3. Non-linear Shrödinger equation (an example)
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study 22 128
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 Written Exams 0 100
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: