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PHYS 5093: Group Theory in Quantum Mechanics

PHYS 5093: Group Theory in Quantum Mechanics (Spring 2015, University of Arkansas). 2015 Physics lectures from the University of Arkansas - Fayetteville, AR. These videos are a component of the graduate course PHYS 5093 (502V) - "Group Theory in Quantum Mechanics". The principle texts are "Quantum Theory in the Computer Age" & "Principles of Symmetry, Dynamics, and Spectroscopy". These were both written by Prof. William G. Harter.

The course utilizes the principles and applications of symmetry analysis to better understand the behavior and spectroscopy of atomic and molecular systems, using symmetry, group representation theory, and Fourier analysis. We attempt to present the mathematical analysis as a consequence of the physical reality, instead of the other way around. This approach helps clarifies the relationship between mathematics and physics, as well as, aids in retention and recall. It is hoped that the techniques and methodologies presented lead to an increased understanding of physics, and illustrate their inherent advantages in computation.

Introduction to Quantum Amplitudes and Analyzers


Lecture 01 - Introduction to Quantum Amplitudes and Analyzers
Lecture 02 - Quantum Amplitudes, Analyzers, and Axioms
Lecture 03 - Analyzers, Operators, and Group Axioms
Lecture 04 - Matrix Eigensolutions and Spectral Decompositions
Lecture 05 - Spectral Decomposition with Repeated Eigenvalues
Lecture 06 - Spectral Decomposition of Bi-Cyclic Operators
Lecture 07 - Spectral Analysis of U(2) Operators
Lecture 08 - Spinor and Vector Representations of U(2) and R(3) Operators
Lecture 09 - Applications of U(2) and R(3) Representations I
Lecture 10 - Applications of U(2) and R(3) Representations II
Lecture 11 - Representations of Cyclic Groups C3⊂C6⊃C2
Lecture 12 - Symmetry and Dynamics of CN Cyclic Systems I
Lecture 12.5 - Symmetry and Dynamics of CN Cyclic Systems II
Lecture 12.6 - Symmetry and Dynamics of CN Cyclic Systems III
Lecture 13 - CN Symmetry Systems Coupled, Uncoupled, and Recoupled
Lecture 14 - Smallest Non-Abelian Group D3 (and Isomorphic D3v~D3)
Lecture 15 - Spectral Decomposition of Groups D3~D3v
Lecture 16 - Local-Symmetry Eigensolutions and Vibrational Modes
Lecture 17 - Vibrational Modes and Symmetry Reciprocity
Lecture 18 - Hexagonal D6⊂D6h and Octahedral-Tetrahedral O~Td Symmetry
Lecture 19 - Octahedral-Tetrahedral O~Td Symmetries
Lecture 20 - Octahedral-Tetrahedral O~Td Representations and Spectra
Lecture 21 - Octahedral-Tetrahedral Oh⊃ Subgroup Tunneling Parameter Modeling
Lecture 22 - Harmonic Oscillator Symmetry U(1)⊂U(2)⊂U(3) I
Lecture 23 - Harmonic Oscillator Symmetry U(1)⊂U(2)⊂U(3) II
Lecture 24 - Rotational Symmetry U(2)⊂U(3) and O(3)
Lecture 25 - Introduction to Rotational Eigenstates and Spectra I
Lecture 26 - Introduction to Rotational Eigenstates and Spectra II
Lecture 27 - Introduction to Rotational Eigenstates and Spectra III

References
Group Theory in Quantum Mechanics (Spring 2015)
Text: Quantum Theory in the Computer Age. Text: Principles of Symmetry, Dynamics, and Spectroscopy. Lecture Slides. Related Paper and Talks.