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Programme & Unit Catalogues

## PH40073: Mathematical physics

Owning Department/School: Department of Physics
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period: Semester 2
Assessment: EX 100%
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take PH20029 OR take PH20067
Description: Aims:
The aim of this unit is to develop students' understanding of some fundamental aspects of Physics, where a mathematical treatment is essential fully to appreciate the subject. For the section on phase transitions, the aim is for students to gain a quantitative understanding of the principles that govern first and second order phase transitions. For the section on classical mechanics, the aim is for students to understand and apply the Lagrangian formulation of classical mechanics.

Learning Outcomes:
After taking the section on phase transitions the student should be able to:
* perform mean field calculations of phase transitions;
* define critical exponents and discuss scaling relations and universality classes;
* describe in detail the principles of real-space renormalisation;
After taking the section on classical mechanics the student should be able to:
* show proficiency in using the Lagrangian and Hamiltonian formulations to solve problems in classical mechanics;
* use symmetries to derive conservation laws;
* formulate and analyse equations of motion for systems of oscillators;
* analyse nonlinear field models using methods of classical mechanics.

Skills:
Numeracy T/F A, Problem Solving T/F A.

Content:
Phase transitions: Phenomenology, classification of phase transitions. Mean field theories; Weiss theory, Landau theory, Van der Waals theory. Statistical mechanics of phase transitions; examples based on the Ising model. Introduction to scaling and the renormalisation group.
Classical mechanics: Calculus of variations. Hamilton's principle, Lagrangian formulation of classical mechanics, examples. Symmetry and conservation laws. Linear and non-linear dynamics. Classical field theory. Non-linear wave equations.
Programme availability:

#### PH40073 is Compulsory on the following programmes:

Department of Physics
• USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 3)
• USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 4)
• USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 4)

#### PH40073 is Optional on the following programmes:

Department of Physics
• USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 3)
• USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
• USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)
• USPH-AFM02 : MPhys(Hons) Physics (Year 4)
• USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 4)
• USPH-AKM11 : MPhys(Hons) Physics with Astrophysics with Professional and Research Placements (Year 5)
• USPH-AKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 5)
• USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 4)
• USPH-AAM10 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 4)
• USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 5)
• USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 5)
• USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 4)
• USPH-AAM03 : MPhys(Hons) Physics with Study year abroad (Year 4)
• USPH-AAM12 : MPhys(Hons) Physics with Study year abroad (Year 5)

 Notes: This unit catalogue is applicable for the 2020/21 academic year only. Students continuing their studies into 2021/22 and beyond should not assume that this unit will be available in future years in the format displayed here. Programmes and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules. Undergraduates: Find out more about these and other important University terms and conditions here. Postgraduates: Find out more about these and other important University terms and conditions here.