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September 23, 2023

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Description

Group Theory Methods in Physics. Instructor: Prof. P. Ramadevi, Department of Physics, IIT Bombay.

This course is a first course pitched at UG level so that the students can appreciate the wide applications of the group theory tools in other areas of Physics. Topics covered in this course include: introduction to discrete groups, subgroups and generators, conjugacy classes, symmetric groups, permutation group, cycle notation, direct product groups, semi-direct product groups, symmetries of molecules, point groups and stereographic projection, matrix representation of groups, Reducible and irreducible representation, great orthogonality theorem and character tables, Mulliken notation, tensor product, projection operator, observables, selection rules, Molecular vibrations, continuous groups, Lorentz transformations, orthogonal groups and Lie algebra, Wigner-Eckart theorem, hydrogen atom, and dynamical symmetry. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Introduction I Unlimited
  • Lecture 02 – Introduction II Unlimited
  • Lecture 03 – Normal Subgroup, Coset, Conjugate Group Unlimited
  • Lecture 04 – Factor Group, Homomorphism, Isomorphism Unlimited
  • Lecture 05 – Factor Group, Homomorphism, Isomorphism (cont.) Unlimited
  • Lecture 06 – Conjugacy Classes Unlimited
  • Lecture 07 – Permutation Groups Unlimited
  • Lecture 08 – Cycle Structure Unlimited
  • Lecture 09 – Cycle Structure (cont.) Unlimited
  • Lecture 10 – Young Diagram and Molecular Symmetry Unlimited
  • Lecture 11 – Point Groups Unlimited
  • Lecture 12 – Symmetries of Molecules, Schoenflies Notation Unlimited
  • Lecture 13 – Symmetries of Molecules, Stereographic Projection Unlimited
  • Lecture 14 – Examples of Molecular Symmetries and Proof Cayley Theorem Unlimited
  • Lecture 15 – Matrix Representation of Groups I Unlimited
  • Lecture 16 – Matrix Representation of Groups II Unlimited
  • Lecture 17 – Reducible and Irreducible Representation I Unlimited
  • Lecture 18 – Reducible and Irreducible Representation II Unlimited
  • Lecture 19 – Great Orthogonality Theorem and Character Table I Unlimited
  • Lecture 20 – Great Orthogonality Theorem and Character Table II Unlimited
  • Lecture 21 – Mulliken Notation, Character Table and Basis Unlimited
  • Lecture 22 – Tensor Product of Representation Unlimited
  • Lecture 23 – Tensor Product and Projection Operator I Unlimited
  • Lecture 24 – Tensor Product and Projection Operator II Unlimited
  • Lecture 25 – Tensor Product and Projection Operator with an Example Unlimited
  • Lecture 26 – Binary Basis and Observables Unlimited
  • Lecture 27 – Selection Rules Unlimited
  • Lecture 28 – Selection Rules and Molecular Vibrations Unlimited
  • Lecture 29 – Molecular Vibration Normal Modes: Classical Mechanics Approach Unlimited
  • Lecture 30 – Molecular Vibration Normal Modes: Group Theory Approach Unlimited
  • Lecture 31 – Molecular Vibration Modes using Projection Operator Unlimited
  • Lecture 32 – Vibrational Representation of Character Unlimited
  • Lecture 33 – Infrared Spectra and Raman Spectra Unlimited
  • Lecture 34 – Introduction to Continuous Group Unlimited
  • Lecture 35 – Generators of Translational and Rotational Transformation Unlimited
  • Lecture 36 – Generators of Lorentz Transformation Unlimited
  • Lecture 37 – Introduction to O(3) and SO(3) Group Unlimited
  • Lecture 38 – SO(n) and Lorentz Group Unlimited
  • Lecture 39 – Generalised Orthogonal Group and Lie Algebra Unlimited
  • Lecture 40 – Subalgebra of Lie Algebra Unlimited
  • Lecture 41 – gl(2,C) and sl(2,C) Group Unlimited
  • Lecture 42 – U(n) and SU(n) Group Unlimited
  • Lecture 43 – Symplectic Group Unlimited
  • Lecture 44 – SU(2) and SU(3) Groups Unlimited
  • Lecture 45 – Rank, Weight and Weight Vector Unlimited
  • Lecture 46 – Weight Vector, Root Vector, Comparison between SU(2) and SU(3) Algebra Unlimited
  • Lecture 47 – Root Diagram, Simple Roots, Adjoint Representation Unlimited
  • Lecture 48 – SU(2) Subalgebra, Dynkin Diagrams Unlimited
  • Lecture 49 – Fundamental Weights, Young Diagrams, Dimension of Irreducible Representation Unlimited
  • Lecture 50 – Young Diagrams and Tensor Products Unlimited
  • Lecture 51 – Tensor Product, Wigner-Eckart Theorem Unlimited
  • Lecture 52 – Tensor Product of Irreducible Representation 1: Composite Objects from … Unlimited
  • Lecture 53 – Tensor Product of Irreducible Representation 2: Decimet and Octet Diagrams … Unlimited
  • Lecture 54 – Clebsch-Gordan Coefficients Unlimited
  • Lecture 55 – Quadrupole Moment Tensor (Wigner-Eckart Theorem), … Unlimited
  • Lecture 56 – Higher Dimensional Multiplets in the Quark Model Unlimited
  • Lecture 57 – Symmetry Breaking in Continuous Groups Unlimited
  • Lecture 58 – Dynamical Symmetry in Hydrogen Atom: SO(4) Algebra Unlimited
  • Lecture 59 – Hydrogen Atom Energy Spectrum and Degeneracy using Runge-Lenz Vector Unlimited

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