Group Theory in Quantum Mechanics
Spring 2013 PHYS-5093
2013 Text Topics
Detailed Text Listing
Preface
Comparison of Quantum Mechanics Texts
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)
2013 Lecture Topics
Un-proofed
Detailed Lecture Listing
Lecture 1.
Introduction to quantum amplitudes and analyzers
(1.15.13)
Lecture 2.
Quantum amplitudes, analyzers, and axioms
(1.17.13)
Lecture 3.
Analyzers, operators, and group axioms
(1.22.13)
Lecture 4.
Matrix Eigensolutions and Spectral Decompositions
(1.24.13)
Lecture 5.
Spectral Decomposition with Repeated Eigenvalues
(1.29.13)
Lecture 6.
Spectral Decomposition of Bi-Cyclic (C
2
⊂U(2)) Operators
(1.31.13)
Lecture 7.
Spectral Analysis of U(2) Operators
(2.5.13)
Lecture 8.
Spinor and vector representations of U(2) and R(3) Operators
(2.7.13)
Lecture 9.
Applications of U(2) and R(3) representations
(2.12.13)
Lecture 10.
Representations of cyclic groups C
3
<⊂ C
6
⊃ C
2
(2.26.13)
Lecture 11.
Symmetry and Dynamics of C
N
cyclic systems
(2.19-28 to 3.5.13)
Lecture 12.
C
N
symmetry systems coupled, uncoupled, and re-coupled
(3.7.13)
Lecture 13.
Smallest non-Abelian isomorphic groups D
3
~C
3v
(IJMS p.755-774, GTQM Unit 5 Ch. 15 , PSDS Ch. 3)
(3.12.13)
Lecture 14.
Spectral decomposition of groups D
3
~C
3v
(IJMS p.755-774, GTQM Unit 5 Ch. 15, PSDS Ch. 3 )
(3.14.13)
Lecture 15.
Projector algebra and Hamiltonian local-symmetry eigensolution
(IJMS p.755-774, GTQM Unit 5 Ch. 1, PSDS Ch. 4)
(3.26.13)
Lecture 16.
Local-symmetry eigensolutions and vibrational modes
(IJMS p.755-774, GTQM Unit 5 Ch. 15, PSDS Ch. 4)
(3.28.13)
Lecture 17.
Vibrational modes and symmetry reciprocity: Induced reps
(IJMS p.755-774, GTQM Unit 5 Ch. 15, PSDS Ch. 4)
(4.2.13)
Lecture 18.
Hexagonal D
6
⊂ D
6h
and octahedral-tetrahedral O~T
d
symmetry
(IJMS p.755, GTQM Unit 5 Ch. 15, PSDS Ch. 4)
(4.4.13)
Lecture 19.
Octahedral-tetrahedral O~T
d
symmetries
(IJMS p.755-774, GTQM Unit 5 Ch. 15, PSDS Ch. 4)
(4.9.13)
Lecture 20.
Octahedral-tetrahedral O~T
d
representations and spectra
(IJMS p.755-774, GTQM Unit 5 Ch. 15, PSDS Ch. 4)
(4.11.13)
Lecture 21.
Octahedral O
h
⊃O⊃D
4
⊃C
4
eiegensolution in coset spaces
(IJMS p.755-774, GTQM Unit 5 Ch. 15, PSDS Ch. 4 )
(4.16.13)
Lecture 22.
Octahedral O
h
⊃O⊃D
4
⊃C
4
eiegensolution in coset spaces II
(IJMS p.755-774, GTQM Unit 5 Ch. 15, PSDS Ch. 4)
(4.18.13)
Lecture 23.
Octahedral-tetrahedral O~T
d
symmetries
(IJMS p.755-774, GTQM Unit 5 Ch. 15, PSDS Ch. 4)
(4.23.13)
Lecture 24.
Harmonic oscillator symmetry U(1)⊂U(2)⊂
U(3)...
(IJMS p.755-774, GTQM Unit 7 Ch. 21-22 , PSDS Ch. 8)
(4.25.13)
Lecture 25.
Rotational symmetry U(2)⊂U(3) and R(3)
(IJMS p.755-774, GTQM Unit 7 Ch. 21-22 , PSDS Ch. 5, 7)
(4.30.13)
Lecture 26.
Symmetry product analysis U(m)*S
n
tensors
(IJMS p.755-774, GTQM Unit 7 Ch. 23-26 , PSDS Ch. 5, 7)
(5.2.13)
Listings of Other Classes
2012 PHYS 3614 Modern Physics
2013 PHYS 5103 Classical Mechanics
2014 PHYS 5513 Atomic, Molecular, and Optical Physics
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