Quantum Mechanics: Elementary Concepts

This online course is ideal for beginners in quantum mechanics. Designed with modest mathematical prerequisites, it offers a clear and hands-on introduction to the subject. Through a combination of video lectures, visualizations, and specially crafted exercises, you will develop a solid understanding of the fundamental principles of quantum mechanics from the ground up.

If you have a basic understanding of complex numbers and calculus, you should be well-prepared for this course.

The concepts covered in this course include quantum states, wave functions, Schrödinger's equation, observables, expectation values, Heisenberg's uncertainty principle, zero-point energy, the superposition principle, Schrödinger's cat states, stationary states, energy quantization, measurements, Born's rule, wave function collapse, free motion, oscillations, scattering, and tunneling.

Enjoy your quantum journey!

Course material

🎞️ Lesson 1: Schrödinger's equation
🎞️ Lesson 2: Example system: Harmonic oscillator - part 1
✍️ Exercise 1: Coherent state of a harmonic oscillator
🎞️ Lesson 3: Example system: Harmonic oscillator - part 2
🎞️ Lesson 4: Born's rule
🎞️ Lesson 5: Normalization condition
✍️ Exercise 2: An example of using the Born rule
🎞️ Lesson 6: Position expectation value
✍️ Exercise 3: Position expectation value in symmetric distributions
✍️ Exercise 4: Position expectation value: An example
🎞️ Lesson 7: Momentum expectation value
✍️ Exercise 5: Momentum expectation value
✍️ Exercise 6: Mean momentum of a particle with a real wave function
🎞️ Lesson 8: Observables and operators
🎞️ Lesson 9: Zero-point energy of a harmonic oscillator
✍️ Exercise 7: Expectation values of x, p, V, and T for a coherent state
🎞️ Lesson 10: Uncertainty
✍️ Exercise 8: An example of Heisenberg's uncertainty principle
🎞️ Lesson 11: Heisenberg's uncertainty principle
✍️ Exercise 9: Derivation of Heisenberg’s uncertainty principle
🎞️ Lesson 12: Zero-point energy revisited
🎞️ Lesson 13: Quantum superposition
✍️ Exercise 10: Normalizing a cat state
🎞️ Lesson 14: Stationary states - part 1
🎞️ Lesson 15: Stationary states - part 2
🎞️ Lesson 16: Particle in a box
✍️ Exercise 11: Normalization constant for the stationary states of a particle in a box
✍️ Exercise 12: Classical limit in the particle-in-a-box system
🎞️ Lesson 17: Origin of motion
✍️ Exercise 13: Temporal oscillations in a superposition of two stationary states
✍️ Exercise 14: Determining expansion coefficients from the initial wave function
🎞️ Lesson 18: Expansion coefficients, energy measurement, wave function collapse
✍️ Exercise 15: An alternative form of the normalization condition
✍️ Exercise 16: Two alternative expressions for the expectation value of energy
✍️ Exercise 17: Energy measurement for a particle in a box
🎞️ Lesson 19: Free particle
✍️ Exercise 18: Free-particle Gaussian wave packet
🎞️ Lesson 20: Step potential
✍️ Exercise 19: Solving the Schrödinger equation for the step potential
✍️ Exercise 20: Step potential: Probabilities of reflection and transmission
🎞️ Lesson 21: Quantum tunneling
✍️ Exercise 21: Tunneling through a rectangular potential barrier