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: MachZehder Interferometer, ElitzurVaidman 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 Onedimensional Potentials

10

Solving the TimeIndependent 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{{< sub “0” >}}, Step Potential with E < V{{< sub “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: Onedimensional 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)
