Quantum Mechanics: From Wavefunctions to Qubits
From Wavefunctions to Qubits
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40 chapters
~66 hours total
303 sections
1
Front Matter
4 chapters2
Part I: Foundations — Wave Mechanics
8 chapters- Part I: Foundations — Wave Mechanics
- Chapter 1: The Quantum Revolution: Why Classical Physics Broke and What Replaced It
- Chapter 2: The Wave Function and the Schrödinger Equation — The Rules of the Game
- Chapter 3: Solving the Schrödinger Equation — The Infinite Square Well and Other Exactly Solvable Problems
- Chapter 4: The Quantum Harmonic Oscillator — The Most Important Problem in All of Physics
- Chapter 5: Quantum Mechanics in Three Dimensions: The Hydrogen Atom
- Chapter 6: The Formalism — Operators, Commutators, and the Generalized Uncertainty Principle
- Chapter 7: Time Evolution and the Schrödinger vs. Heisenberg Pictures
3
Part II: The Mathematics of Quantum Mechanics
5 chapters- Part II: The Mathematics of Quantum Mechanics
- Chapter 8: Linear Algebra for Quantum Mechanics — Vector Spaces, Operators, and Dirac Notation
- Chapter 9: Eigenvalue Problems and Spectral Theory — How Measurement Works Mathematically
- Chapter 10: Symmetry and Conservation Laws — Why Quantum Mechanics Loves Group Theory
- Chapter 11: Tensor Products and Composite Systems — How Quantum Systems Combine
4
Part III: Angular Momentum and Spin
6 chapters- Part III: Angular Momentum and Spin
- Chapter 12: Angular Momentum Algebra: Raising, Lowering, and the General Theory
- Chapter 13: Spin — The Quantum Property with No Classical Analogue
- Chapter 14: Addition of Angular Momentum — Clebsch-Gordan Coefficients and Coupled Representations
- Chapter 15: Identical Particles — Bosons, Fermions, and the Pauli Exclusion Principle
- Chapter 16: Multi-Electron Atoms and the Building of the Periodic Table
5
Part IV: Approximation Methods
7 chapters- Part IV: Approximation Methods
- Chapter 17: Time-Independent Perturbation Theory — The Non-Degenerate Case
- Chapter 18: Degenerate Perturbation Theory and Fine Structure of Hydrogen
- Chapter 19: The Variational Principle: When You Can't Solve It, Bound It
- Chapter 20: The WKB Approximation: Semiclassical Quantum Mechanics
- Chapter 21: Time-Dependent Perturbation Theory: Transitions and Radiation
- Chapter 22: Scattering Theory: Quantum Collisions
6
Part V: Modern Quantum Mechanics
6 chapters- Part V: Modern Quantum Mechanics
- Chapter 23: The Density Matrix and Mixed States: Quantum Mechanics Beyond Pure States
- Chapter 24: Entanglement, Bell's Theorem, and the Foundations of Quantum Mechanics
- Chapter 25: Quantum Information and Computation: The Qubit and Beyond
- Chapter 26: QM in Condensed Matter: Bands, Semiconductors, and Superconductivity
- Chapter 27: Quantum Mechanics of Light — Photons, Coherent States, and Quantum Optics
7
Part VI: Advanced Topics and Extensions
4 chapters8
Part VII: The Frontiers and the Big Questions
8 chapters- Part VII: The Frontiers and the Big Questions
- Chapter 31: Path Integrals — Feynman's Formulation
- Chapter 32: The Adiabatic Theorem and Berry Phase
- Chapter 33: Open Quantum Systems and Decoherence
- Chapter 34: Second Quantization — From Particles to Fields
- Chapter 35: Quantum Error Correction
- Chapter 36: Topological Phases of Matter — When Geometry Becomes Destiny
- Chapter 37: From Quantum Mechanics to Quantum Field Theory
9
Part VIII: Capstones
4 chapters10
Appendices
10 chapters- Appendix A: Mathematical Reference for Quantum Mechanics
- Appendix B: Python Quantum Simulation Toolkit
- Appendix C: Physical Constants and Unit Conversions
- Appendix D: Notation Guide
- Appendix E: Python Environment Setup
- Appendix F: Key Experiments in Quantum Mechanics
- Appendix G: Answers to Selected Exercises
- Appendix H: Glossary of Key Terms
- Appendix I: Index
- Appendix J: Bibliography and Recommended Reading
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