Learning path
Quantum mechanics, the course companion
“I am taking quantum mechanics and I want to see what the equations mean.”
Undergraduate physics, chemistry and engineering students. Follows the order of a typical first QM course, from the old quantum theory to spin and identical particles.
4 milestones · 19 steps · 12 minutes of reading, plus hands-on time
By the end, you will be able to
- Connect each textbook equation to a behaviour you have watched happen
- Solve bound-state problems with intuition for the answer before the algebra
- Reason about uncertainty as a Fourier trade-off, not a measurement flaw
- Handle spin, mixed states and identical particles with confidence
Milestone 1: The old quantum theory
4 stepsYou know which experiments forced quantisation, and what each one showed.
- VisualizationIntermediateModels of the Hydrogen Atom
Bohr, then Schrödinger: why the spectrum has lines.
- VisualizationIntermediateDavisson–Germer: Electron Diffraction
Matter has a wavelength too — de Broglie, measured.
Milestone 2: The Schrödinger equation at work
6 stepsYou can predict the shape of a bound state before you solve for it.
- VisualizationBeginnerParticle in a Box
The infinite and finite square well — chapter two of every textbook.
- VisualizationIntermediateThe Quantum Harmonic Oscillator
The single most reused model in physics, with its ladder of levels.
- VisualizationIntermediateWave Packets and Scattering
Time evolution, dispersion and scattering, animated.
- VisualizationIntermediateUncertainty as a Fourier Trade-off
Heisenberg as a property of Fourier transforms.
- Auto-tracks
- VisualizationIntermediateAlpha Decay: Tunneling with a Half-life
Tunnelling explaining half-lives across twenty orders of magnitude.
Milestone 3: Spin and measurement
4 stepsYou are fluent in two-level systems, the language of the rest of the subject.
- VisualizationBeginnerThe Stern-Gerlach Experiment
Spin-½, discovered by accident, and sequential measurements.
- VisualizationBeginnerThe Bloch Sphere
Every spin-½ state as one point, every operation as one rotation.
- VisualizationAdvancedWavefunctions in Three Dimensions
Orbitals in three dimensions, the way chemistry needs them.
Milestone 4: Beyond the first course
5 stepsYou are ready for the topics second courses and research groups assume.
- VisualizationAdvancedFermions and Bosons
Fermions, bosons and the exchange symmetry behind the periodic table.
- VisualizationAdvancedMixed States and the Density Matrix
Mixed states: the formalism for anything that touches an environment.
- VisualizationAdvancedPhase Space and the Wigner Function
Quantum mechanics in phase space, negativity and all.
Progress is stored in this browser only. Lessons tick themselves when you finish them and challenges when you solve them; everything else you tick yourself, because opening a page is not the same as understanding it.
After this path
- Keep the visualizations open while you do problem sets — changing one parameter beats reading one more paragraph.
- Move on to the Quantum hardware researcher path when you reach open quantum systems.