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Lecture 37 of 68Week 8
Lecture 37 : Introduction to O(3) and SO(3) group
Prof. P. Ramadevi · IIT Bombay
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All the lectures
- Lecture 1 : Introduction I
- Lecture 2 : Introduction II
- Lecture 3 : Normal subgroup, Coset, Conjugate group
- Lecture 4 : Factor group, Homomorphism, Isomorphism
- Lecture 5 : Factor group, Homomorphism, Isomorphism
- Lecture 6 : Conjugacy Classes
- Lecture 7 : Permutation Groups
- Lecture 8 : Cycle Structure
- Lecture 9 : Cycle Structure Continued
- 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 of 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) sub-algebra, 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 : 1) Quadrupole moment tensor (Wigner-Eckart theorem) 2) Decimet Baryon wavefunction
- 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
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