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PHY807 Topics in Mathematical Physics

Campus

SNS

Programs

PG

Session

Fall Semester 2016

Course Title

Topics in Mathematical Physics

Course Code

PHY807

Credit Hours

30

PreRequisutes


Course Objectives

Objectives:
To introduce MPhil students to basic Group Theory and Differential Equations
Outcomes: Students will understand
 How symmetries are related to Group Theory
 Applications of finite groups in physics
 Applications of Lie Groups in Physics
 Use of Differential Equations in Modeling
 Solution of higher order Differential equations
 Application of partial Differential Equations in Electromagnetism and Quantum Mechanics

Detail Content

Groups, Subgroups, Cosets, Lagrange's theorem, Conjugate classes, invariant subgroups Review of linear vector spaces, Representations, Characters
Unitary spaces, Unitary representations, Schur's lemmas, Orthogonality relations, Irreducibility criteria Group algebra, Lie groups with examples. Infinitesimal operators with examples, Lie algebra, Casimir Operators. The rotation group, Irreducible representations and characters of the rotation group. Angular momentum in Quantum Mechanics, SU(2) and its representations. Review of the first order ODEs, Solution of coupled first order ODEs. Use of Differential Equations in modeling with examples
Higher order ODEs, Complementary and particular solutions, Some special ODEs, homogeneous equations. Partial Differential equations with examples. Separation of variables with examples, Laplace equation in spherical polar coordinates, Poisson equation in rectangular coordinates. Series solution about an ordinary point, Legendre's differential equation. Series solution about a singular point, hydrogen atom

Text/Ref Books

Main Texts
 Title: Mathematical Methods for Physics and Engineering
Authors: K.F.Riley, M.P.Hobson and S.J.Bence
Publisher: Cambridge University Press (2006)
 Title: Group Theory and its Applications to Physical Problems
Author: M. Hamermesh
Publisher: Dover Publications (1989)
Reference Books:
 Title: Advanced Engineering Mathematics
Author: Erwin Kreyszig
Publisher: John Wiley and Sons, INC(1999).
 Title: Group Theory
Author: F. Aryasetiawan
Publisher: This is an Ebook

Time Schedule

Fall Semester 2014

Faculty/Resource Person

Dr. Qurat Ul Ain Javed
PhD, University of Science and Technology, Beiging, China
Discipline: Condensed Matter Physics

