Lecture Notes

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 > V0, Step Potential with E < V0, 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)