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Group Theory in Quantum Mechanics
Spring 2017 PHYS-5093

Comparison of Quantum Mechanics Texts      

Outline & Cross-reference  

Text: Quantum Theory in the Computer Age Detailed Text Listing
Unit 1. Introduction to Quantum Amplitudes
Unit 2. Introduction to Wave Dynamics
Unit 3. Introduction to Fourier Analysis and Symmetry
Unit 4. Introduction to Wave Equations
Unit 5. Introduction to Periodic Potentials and Symmetry
Unit 6. Introduction to Time-Variable Perturbations and Transitions
Unit 7. Quantum Harmonic Oscillators
Unit 8. Quantum Rotation and Angular Momentum
Unit 9. Quantum Orbitals and Central force dynamics (In preparation)
Unit 10. Multiparticle States and Interactions (In preparation)
Unit 11. Polyatomic Molecules (In preparation)
Unit 12. Relativistic Spin and Symmetry (Proposed)
Unit 13. Relativistic Quantum Field Theory (Proposed)

Text: Principles of Symmetry, Dynamics, and Spectroscopy
Title & Preface
Chapter 1. A Review of Matrix Algebra and Quantum Mechanics
Chapter 2. Basic Theory and Applications of Symmetry Representations (Abelian Symmetry Groups)
Chapter 3. Basic Theory and Applications of Symmetry Representations (Non-Abelian Symmetry Groups)
Chapter 4. Theory and Applications of Higher Finite Symmetry and Induced Representations
Chapter 5. Representations of Continuous Rotation Groups and Applications
Chapter 6. Theory and Applications of Symmetry Representation Products (Finite Groups)
Chapter 7. Theory and Applications of Symmetry Representation Products (Continuous Rotation Groups)
Chapter 8. Symmetry Analysis for Semiclassical and Quantum Mechanics: Dynamics with High Quanta
Appendix F. Formulas and Tables of Group Representations and Related Quantities
Appendix G. Schur's Lemma and Irreducible Representations and Orthogonality
Index. PSDS Index and PSDS⇔CTCA Page⇔Chapter/Section Cross-Reference Strips
Lectures     2017 Detailed Lecture Listing     2015 Site     2013 Site
Lecture 1. Introduction to quantum amplitudes and analyzers (1.17.17)  View on YouTube From 2015
Lecture 2. Quantum amplitudes, analyzers, and axioms (1.19.17)  View on YouTube
Lecture 3. Analyzers, operators, and group axioms (1.24.17)  View on YouTube
Lecture 4. Matrix Eigensolutions and Spectral Decompositions (1.26.17)  View on YouTube
Lecture 5. Spectral Decomposition with Repeated Eigenvalues (1.31.17)  View on YouTube
Lecture 6. Spectral Decomposition of Bi-Cyclic (C2 ⊂ U(2)) Operators (2.2.17)  View on YouTube
Lecture 7. Spectral Analysis of U(2) Operators (2.7.17)  Part 1View on YouTube Part 2View on YouTube
Lecture 8. Spinor and vector representations of U(2) and R(3) Operators (2.9.17)  Part 1View on YouTube Part 2View on YouTube
Lecture 9. Applications of U(2) and R(3) representations I (2.14.17)  Part 1View on YouTube Part 2View on YouTube
Lecture 10. Applications of U(2) and R(3) representations II (2.16.17)  View on YouTube
Lecture 11. Representations of cyclic groups C3 ⊂ C6 ⊃ C2 (2.21.17)  View on YouTube
Lecture 12. Symmetry and Dynamics of CN cyclic systems I. (2.23.17)  Part 1View on YouTube Part 2View on YouTube
Lecture 12.5. Dynamics of Group vs. Phase Waves and space-time lattices (2.23.17)
Lecture 13. Symmetry and Dynamics of CN cyclic systems II. (2.28.17)  Part 1View on YouTube Part 2View on YouTube
Lecture 14. CN symmetry systems coupled, uncoupled, and re-coupled I. (3.2.17)  View on YouTube
Lecture 14.5 CN symmetry systems coupled, uncoupled, and re-coupled II. (3.7.17)  Part 1View on YouTube Part 2View on YouTube
Lecture 15. Smallest non-Abelian group D3 (and isomorphic C3v ~ D3) (3.9.17)  Part 1View on YouTube Part 2View on YouTube
Lecture 16. Spectral decomposition of groups D3 ~C3v (3.14.17)  Part 1View on YouTube Part 2View on YouTube
Lecture 17. Projector algebra and Hamiltonian local-symmetry eigensolution (3.16.17)  Part 1View on YouTube Part 2View on YouTube
Spring Break (No classes on 3.21.17 & 3.23.17)
Lecture 18. Projector algebra and Hamiltonian local-symmetry eigensolution (3.28.17)  Part 1View on YouTube Part 2View on YouTube
Lecture 19. Octahedral-tetrahedral O~Td symmetries (3.30.17)  Part 1View on YouTube Part 2View on YouTube
Lecture 18. Vibrational modes and symmetry reciprocity: Induced reps (4.4.17)  Part 1View on YouTube Part 2View on YouTube
Lecture 19. Octahedral-tetrahedral O~Td symmetries (4.6.17)  View on YouTube
Lecture 20. Octahedral-tetrahedral O~Td representations and spectra (4.12.17)  Part 1View on YouTube Part 2View on YouTube
Lecture 21. Octahedral Oh ⊃ subgroup tunneling parameter modeling (4.13.17)  Part 1View on YouTube Part 2View on YouTube
Lecture 22. Harmonic oscillator symmetry U(1) ⊂ U(2) ⊂ U(3) ... (4.18.17)  View on YouTube
Lecture 23. Harmonic oscillator symmetry U(1) ⊂ U(2) ⊂ U(3) ... (4.20.17)  View on YouTube
Lecture 24. Rotational symmetry U(2) ⊂ U(3) and O(3) (4.25.17)
Lecture 25. Introduction to Rotational Eigenstates and Spectra I. (4.27.17)  View on YouTube
Lecture 26. Introduction to Rotational Eigenstates and Spectra II. (5.2.17)  View on YouTube
Lecture 27. Introduction to Rotational Eigenstates and Spectra III. (5.3.17)  View on YouTube
Lecture 28. Rotational energy and eigenstate surfaces for Coriolis dynamics (5.4.17)
Lecture 29. Rotational eigenstates and spin-permutation symmetry (5.5.17)  View on YouTube
Lecture 30. Symmetry product analysis U(m)*Sn tensors (Draft lecture for 5.10.17)  View on YouTube
Assignments
Assignment 1.  Due Thurs. (1/24/2017)   Solutions 1.  
Practice Assignment 2.  Due null  
Assignment 3.  Due Thurs. (2/23/2017)   Solutions 3.  
Assignment 4.  Due Thurs. (3/2/2017)   Solutions 4.  
Assignment 5.  Due Thurs. (3/17/2017)   Solutions 5.  
Assignment 6.  Due Thurs. (3/31/2017)  

Listing of Other Classes
2012 PHYS 3614 Modern Physics
2013 PHYS 5093 Group Theory in Quantum Mechanics
2013 PHYS 5103 Advanced Mechanics
2014 PHYS 5513 Atomic, Molecular, and Optical Physics
2014 PHYS 5103 Advanced Mechanics
2015 PHYS 5093 Group Theory in Quantum Mechanics
2016 PHYS 3922H Honors Colloquium
2016 PHYS 5103 Advanced Mechanics
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International Symposium on Molecular Spectroscopy - Columbus 2004
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International Symposium on Molecular Spectroscopy - Columbus 2008(I)
International Symposium on Molecular Spectroscopy - Columbus 2008(II)
International Symposium on Molecular Spectroscopy - Columbus 2009
International Symposium on Molecular Spectroscopy - Columbus 2010(I)
International Symposium on Molecular Spectroscopy - Columbus 2010(II)
International Symposium on Molecular Spectroscopy - Columbus 2012
Wolfram-Mathworld on Group Theory
Course Survey
The Feynman Lectures on Physics - Caltech 2013
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DAMOP Annual Meeting Web Resources - OSU Columbus, OH 6/10/2015
PHYS 5093 - Applications of Group Theory to Quantum Mechanics description and advertisement, UAF 2017
Eric J. Heller Gallery - Art and Science
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Special Relativity Introduction for General Relativity - UAF 2017 Jan
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Representations of Multidimensional Symmetries in Networks - Harter - JMP Nov. 1974
ResearchGate Contibutions Page - W.G. Harter
RelaWavity Drafts
Special Relativity and Quantum Theory by Ruler and Compass - Current Expanded-Earlier draft
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      Current draft via TeX with reference linking
LearnIt - Physics Web Applications
Comprehensive Listing of Harter-Soft Web Resources for Physics