National University of Sciences and Technology
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PHY-807 Topics in Mathematical Physics
Campus SNS
Programs PG
Session Fall Semester 2016
Course Title Topics in Mathematical Physics
Course Code PHY-807
Credit Hours 3-0
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
  1. Title: Mathematical Methods for Physics and Engineering Authors: K.F.Riley, M.P.Hobson and S.J.Bence Publisher: Cambridge University Press (2006)
  2. Title: Group Theory and its Applications to Physical Problems Author: M. Hamermesh Publisher: Dover Publications (1989)
Reference Books:
  1. Title: Advanced Engineering Mathematics Author: Erwin Kreyszig Publisher: John Wiley and Sons, INC(1999).
  2. Title: Group Theory Author: F. Aryasetiawan Publisher: This is an E-book
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