Detailed Textbook Topics 
Unit 1. Introduction to Quantum Amplitudes  
Chapter 1 Quantum Amplitudes and Analyzers  
Chapter 2 Transformation and Transfer Operators  
Chapter 3 Operator Eigensolutions and Perturbations  
Review: Determinants and permutation classes  

Unit 2. Introduction to Wave Dynamics  
Chapter 4 Waves Viewed by Space and Time: Relativity  
Appendices 4A-B: Old-Fashioned Relativity & Relativistic Space-time Coordinates  
Chapter 5 Waves Viewed by Wavevector and Frequency: Dispersion  
Chapter 6 Multidimensional Waves and Modes  
Review: An “Old-Fashioned” classical approach to relativity  

Unit 3. Introduction to Fourier Analysis and Symmetry  
Chapter 7 Fourier Transformation Matrices  
Chapter 8 Fourier Symmetry Analysis  
Chapter 9 Time Evolution and Fourier Dynamics  
Chapter 10 Two-State Evolution, Coupled Oscillation, and Spin  
Review: Optical ellipsometry and “Spin-control” using U(2) analysis  

Unit 4. Introduction to Wave Equations  
Chapter 11 Difference Equations and Differential Operators  
Chapter 12 Infinite-Well States and Dynamics  
Chapter 13 Step Potential Barriers and Wells  
Review: Scattering and “Quantum well control” using U(2) analysis  

Unit 5. Introduction to Periodic Potentials and Symmetry  
Chapter 14 Multiple Barriers, Eigenchannels, and Resonance Bands  
Chapter 15 Non-Abelian Symmetry Analysis of Periodic Systems  
Chapter 16 Fourier Analysis of Periodic Potentials and States  
Review: Molecular symmetry control inside and out  

Unit 6. Introduction to Time-Variable Perturbations and Transitions  
Chapter 17 Classical Electromagnetic Perturbations  
Chapter 18 Transitions Due to Time-Variable Perturbation  
Chapter 19 Two-State Resonant Transitions  
The observer becomes the observed  

Unit 7. Quantum Harmonic Oscillators  
Chapter 20 One-Dimensional Oscillator States and Dynamics  
Chapter 21 Two-Dimensional Oscillator States and Dynamics  
Chapter 22 Quantum Electromagnetic Field  
Review: Bose-Einsein and Fermi-Dirac symmetries  

Unit 8. Quantum Rotation and Angular Momentum
Chapter 23 Two-Dimensional Oscillator and Quantum Rotation  
Chapter 24 Quantum Theory of Molecular and Nuclear Rotors  
Chapter 25 Quantum Theory of Coupled Spins and Rotors  
Review: The quantum frame inside and out: Mach’s conundrum  

Unit 9. Quantum Orbitals and Central force dynamics (In preparation)  
Chapter 26 Hydrogen-like States and Dynamics  
Chapter 27 Helium-like States and Dynamics
Chapter 28 Rydberg States
Fano’s multichannel quantum defect theory

Unit 10. Multiparticle States and Interactions (In preparation)  
Chapter 29 Unitary-Permutation Symmetry Projection
Chapter 30 Molecular Rovibrational States and Dynamics  
Chapter 31 Atomic n Configurations and Excitation
Xray photoelectron spectroscopy (XPS)

Unit 11 Polyatomic Molecules (In preparation)
Chapter 32 Molecular Orbitals and Vibration
Chapter 33 Rovibrational Fine and Superfine Structure
Chapter 34 Nuclear Hyperfine Structure
Superhyperfine spectroscopy

Unit 12 Relativistic Spin and Symmetry (Proposed)
Chapter 35 Lorentz, Poincare, and Conformal Symmetry
Chapter 36 Dirac Model of Spin
Chapter 37 Electromagnetic Interactions
Advanced potentials

Unit 13 Relativistic Quantum Field Theory (Proposed)