Study information

Methods of Theoretical Physics - 2024 entry

MODULE TITLEMethods of Theoretical Physics CREDIT VALUE15
MODULE CODEPHY3062 MODULE CONVENERProf 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.

Pre-requisite modules: PHY2025 or equivalent module.

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 22 Guided Independent Study 128 Placement / Study Abroad 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching activities 20 20×1-hour lectures
Scheduled learning and teaching activities 2 2×1-hour problems/revision classes
Guided independent study 30 5×6-hour self-study packages
Guided independent study 16 4×4-hour problem sets
Guided independent study 82 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 5×6-hour packages (fortnightly) 1-15 Discussion in class
4 × Problems sets 4 hours per set (fortnightly) 1-15
Solutions discussed in problems classes.

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 0 Written Exams 100 Practical Exams 0
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 1-13 Written, 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
Final Examination Written examination (100%) 1-13 Referral/deferral period

 

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

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 Wednesday 13th March 2024 LAST REVISION DATE Tuesday 14th May 2024
KEY WORDS SEARCH Physics; Method; Integrals; Functions; Theory; Expansion; Laurent; Variational; Calculus; Elements; Variable.

Please note that all modules are subject to change, please get in touch if you have any questions about this module.