Quantum Mechanics I

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Pre-Quantum Mechanics

1. Introduction to Waves (The Wave Equation)
2. Introduction to Waves (The Wave Function)
3. Motivation for Quantum Mechanics (Photoelectric effect)
4. Motivation for Quantum Mechanics (Compton Scattering)
5. Motivation for Quantum Mechanics (Black Body Radiation)
6. Bohr Model of the Atom

Introduction to the Mathematical Framework

7. Wave-Particle Duality (The Wave Function Motivation)
8. Problems with the Wave Function
9. Introduction to Quantum Operators (The Formalism)
10. Introduction to Dirac Notation
11. Introduction to Quantum Operators (The Hermitian and the Adjoint)
12. Introduction to Commutation
13. Expectation Values of Operators
14. Quantum Uncertainty (Defining Uncertainty)
15. Quantum Uncertainty (Heisenberg's Uncertainty Principle)
16. The Schrödinger Equation (The "Derivation")
17. The Schrödinger Equation (How to Use it)
18. No Degeneracy in 1-Dimension
19. Parity Operator
20. Quantum Mechanics' Core Postulates

Solving Quantum Mechanical Problems

21. Free Particle (In a Vacuum)
22. Particle in a Box (Infinite Square Well)
23. Bound States (The Mathematical Setup)
24. Bound States (The Shooting Method)
25. Bound States (Patching Solutions Together)
26. Patching Solutions (Finite, Infinite, and Delta Function Potentials)
27. Delta Function Potential Well
28. Scatter States (A Touch on Dispersion)
29. Scatter States (Reflection, Transmission, Probability Current)
30. Scatter States (Worked Example)
31. Scatter States (Elastic Collision)
32. Quantum Tunneling (Constant Potential)
33. Quantum Tunneling (Changing Potential)
34. Quantum Tunneling (Alpha Decay Example)
35. Quantum Harmonic Oscillator (Classical Mechanics Analogue)
36. Quantum Harmonic Oscillator (Brute Force Solution)
37. Quantum Harmonic Oscillator (Ladder Operators)
38. Quantum Harmonic Oscillator (Expectation Values)

Expanding to 3-Dimensions

39. Bringing Quantum to 3D (Cartesian Coordinates)
40. Free Particle
41. Infinite Cubic Well (3D Particle in a Box)
42. Quantum Harmonic Oscillator
43. Schrödinger Equation (Spherical Coordinates)
44. Angular Momentum (Experiments)
45. Angular momentum (Operators)
46. Angular momentum (Ladder Operators)
47. Schrödinger Equation (Spherically Symmetric Potential)
48. Infinite Spherical Well (Radial Solution)
49. One Electron Atom (Radial Solution for S-orbital)
50. Hydrogen Atom (Angular Solution; Spherically Symmetric)
51. Hydrogen Atom (Radial Solution; Any Orbital)
52. Hydrogen Atom (Recap)