# InfoCoBuild

## Group Theory Methods in Physics

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)

 Lecture 55 - Quadrupole Moment Tensor (Wigner-Eckart Theorem), ...

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