**Part 1: Basic Concepts** |

1 |
Key Features of Quantum Mechanics: Linearity of the Equations of Motion, Complex Numbers are Essential, Loss of Determinism, Quantum Superpositions, Entanglement (PDF) |

2 |
Experiments with Photons: Mach-Zehder Interferometer, Elitzur-Vaidman Bombs (PDF) |

3 |
Particle Nature of Light and Wave Nature of Matter: Photoelectric Effect, Compton Scattering, Matter Waves (PDF) |

4 |
de Broglie Wavelength and Galilean Transformations, Phase and Group Velocities, Choosing the Wavefunction for a Free Particle (PDF) |

5 |
Equations for a Wavefunction, Schrödinger Equation for Particle in a Potential, Interpreting the Wavefunction (PDF) |

6 |
Normalization and Time Evolution, The Wavefunction as a Probability Amplitude, The Probability Current, Probability Current in 3D and Current Conservation (PDF) |

7 |
Wavepackets and Uncertainty, Wavepacket Shape Changes, Time Evolution of a Free Wave Packet (PDF) |

8 |
Uncovering Momentum Space, Expectation Values of Operators, Time Dependence of Expectation Values (PDF) |

9 |
Observables and Hermitian Operators, Uncertainty (PDF) |

**Part 2: Quantum Physics in One-dimensional Potentials** |

10 |
Solving the Time-Independent Schrödinger Equation: Stationary States, Solving for Energy Eigenstates, Free Particle on a Circle (PDF) |

11 |
The Infinite Square Well, The Finite Square Well (PDF) |

12 |
General Properties, Bound States in Slowly Varying Potentials, Sketching Wavefunction Behavior in Different Regions, Shooting Method (PDF - 1.4MB) |

13 |
Delta Function Potential, The Node Theorem, Simple Harmonic Oscillator (PDF - 1.3MB) |

14 & 15 |
Algebraic Approach to the Simple Harmonic Oscillator: Algebraic Solution of the Oscillator, Operator Manipulation and the Spectrum (PDF) |

16 |
Scattering States and the Step Potential: The Step Potential, Step Potential with E > V_{0}, Step Potential with E < V_{0}, Wavepackets in the Step Potential (PDF) |

17 |
Resonant Transmission in a Square Well, The Ramsauer–Townsend Effect (PDF) |

18 |
Scattering in One Dimension: Time Delay, An Example (PDF) |

**Part 3: One-dimensional Scattering, Angular Momentum, and Central Potentials** |

19 |
Levinson’s Theorem, Resonances, Modeling the Resonance (PDF - 1.1MB) |

20 & 21 |
Quantum Mechanics in 3D and Central Potentials: Schrödinger Equation in 3D and Angular Momentum, The Angular Momentum Operator, Eigenstates of Angular Momentum, The Radial Wave Equation (PDF) |

21 & 22 |
Hydrogen Atom, Hydrogen Atom Spectrum (PDF) |