Group Theory in Quantum Mechanics
Spring 2015 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. 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     2015 Detailed Lecture Listing     2013 Info page
Lecture 1. Introduction to quantum amplitudes and analyzers (1.13.15)  View on YouTube
Lecture 2. Quantum amplitudes, analyzers, and axioms (1.15.15)  View on YouTube
Lecture 3. Analyzers, operators, and group axioms (1.20.15)  View on YouTube
Lecture 4. Matrix Eigensolutions and Spectral Decompositions (1.22.15)  View on YouTube
Lecture 5. Spectral Decomposition with Repeated Eigenvalues (1.27.15)  View on YouTube
Lecture 6. Spectral Decomposition of Bi-Cyclic (C2 ⊂ U(2)) Operators (1.29.15)  View on YouTube
Lecture 7. Spectral Analysis of U(2) Operators (2.3.15)  View on YouTube
Lecture 8. Spinor and vector representations of U(2) and R(3) Operators (2.5.15)  View on YouTube
Lecture 9. Applications of U(2) and R(3) representations I. (2.10.15)
Lecture 10. Applications of U(2) and R(3) representations II. (2.12.15)  View on YouTube
Lecture 11. Representations of cyclic groups C3 ⊂ C6 ⊃ C2 (2.19.15)  View on YouTube
Lecture 12. Symmetry and Dynamics of CN cyclic systems I (2.20.15)  View on YouTube
Lecture 12.5 Symmetry and Dynamics of CN cyclic systems II (2.24.15)  View on YouTube
Lecture 12.6. Symmetry and Dynamics of CN cyclic systems III (3.3.15)  View on YouTube
Lecture 13. CN symmetry systems coupled, uncoupled, and re-coupled (3.5.15)  View on YouTube
Lecture 14. Smallest non-Abelian group D3 (and isomorphic C3v ~D3) (3.10.15)  View on YouTube
Lecture 15. Spectral decomposition of groups D3 ~ C3v (3.12.15)  View on YouTube
Lecture 16. Local-symmetry eigensolutions and vibrational modes (3.19.15)  View on YouTube
      Lecture 16 (Detailed). Projector algebra and Hamiltonian local-symmetry eigensolution
Lecture 17. Vibrational modes and symmetry reciprocity: Induced reps (3.20.15)  View on YouTube
Lecture 18. Hexagonal D6⊂D6h and octahedral-tetrahedral O~Td symmetry (3.31.15)  View on YouTube
Lecture 19. Octahedral-Tetrahedral O ~ Td symmetries (4.2.15)  View on YouTube
Lecture 20. Octahedral-Tetrahedral O ~ Td Representations and Spectra (4.7.15)  View on YouTube
Lecture 21. Octahedral Oh⊃subgroup tunneling parameter modeling (4.9.15)  View on YouTube
Lecture 22. Harmonic oscillator symmetry U(1) ⊂ U(2) ⊂ U(3) I. (4.14.15)  View on YouTube
Lecture 23. Harmonic oscillator symmetry U(1) ⊂ U(2) ⊂ U(3) II. (4.17.15)  View on YouTube
Lecture 24. Rotational symmetry U(2) ⊂ U(3) and O(3) (4.21.15)  View on YouTube
Lecture 25. Introduction to Rotational Eigenstates and Spectra I. (4.24.15)  View on YouTube
Lecture 26. Introduction to Rotational Eigenstates and Spectra II. (4.28.15)  View on YouTube
Lecture 27. Introduction to Rotational Eigenstates and Spectra III. (4.30.15)  View on YouTube
Lecture 28. Rotational energy and eigenstate surfaces for Coriolis dynamics (4.30.15)
Lecture 29. Rotational eigenstates and spin-permutation symmetry (4.30.15)
Lecture 30. Symmetry product analysis U(m)*Sn tensors (4.30.15)
Listings of Other Classes
2012 PHYS 3614 Modern Physics
2013 PHYS 5103 Classical Mechanics
2014 PHYS 5513 Atomic, Molecular, and Optical Physics
2014 PHYS 5103 Classical Mechanics
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