How to use this site
How to use the site, how to pick one of the three routes, and the notation used throughout.
After this section you should be able to
- Choose a learning route that suits you
- Know what each page element (collapsible derivation, misconception box, simulation, quiz) is for
- Learn the notation and unit conventions so nothing clashes with your textbook
What this site is
A course in quantum mechanics that runs from no background to the research frontier, with one distinguishing habit: wherever something can be dragged, you get to drag it. Wavefunctions, energy levels and transmission probabilities are computed in your browser on the spot, not pasted in as images.
The whole site is static. There is no account and no server; your progress lives only in this device’s browser. Pages you have already opened stay readable with the network off.
The blocks you will meet
| Element | How to use it |
|---|---|
| Collapsible derivation | Collapsed by default. Skip on a first read and open it when you want to work through the algebra. Tagged basic / advanced / optional with an estimated time |
| Picture vs formalism | Two columns saying the same thing. Read the left when the formula blocks you, the right when you “understand it but cannot compute with it” |
| Common misconception | The red boxes. These are real traps that textbooks usually leave implicit |
| Interactive simulation | Marked with ◈. Predict first, then drag, or you are only watching an animation |
| Quiz | Immediate feedback that tells you where a wrong answer went wrong. Retake freely |
| Self-assessment | At the end of each section; the result shows up in the contents tree on the left |
Keyboard shortcuts
| Key | Action |
|---|---|
/ or Ctrl/Cmd + K | Open search |
← → | Previous / next section |
f | Formula reference panel |
t | Toggle dark / light |
Three routes
Same content, different order. Which one fits depends on what you are currently missing.
The picture
01 → 02 → 05 → 06 → 03 → 07 → 08
Settle “why quantum mechanics is needed at all” first, build intuition with one-dimensional problems and spin, and only then go back for the formalism. Look up mathematical tools in appendix A when you need them.
Leaving chapter 3 until late looks odd, but by then you will have worked through a pile of examples by hand, and Dirac notation will read as “a shorter way to write what you already know” rather than abstraction out of nowhere.
The mathematics
Undergraduates meeting quantum mechanics for the first time, self-learners, and anyone who took a course and is left holding a pile of formulas.
The cost: there will be a stretch where your tools feel inadequate (adding angular momenta, for instance). Sit with it; chapter 3 pays the debt off in one go.
The picture
03 → 02 → 04 → 05 → 06 → 07 → 08
Start from Hilbert space and the postulates, and treat one-dimensional problems as worked examples of the formalism. This is how most graduate courses run.
The mathematics
People with solid linear algebra who are comfortable starting from axioms.
The cost: it easily becomes “I can compute but I do not know what I am computing”. Play with at least one simulation per chapter as an anchor for intuition.
The picture
02 → 03 → 05 → 09 → 10 → 13
Skip the continuum, hydrogen and approximation methods; go for two-level systems, entanglement, algorithms and error correction. From chapter 5 you only need the spin sections (5.3–5.5).
The mathematics
People aiming squarely at quantum computing or quantum information.
The cost: what you skipped — especially time-dependent perturbation theory and the physical origin of open-system behaviour — will come looking for you when you read hardware papers. Chapters 6–8 can be picked up at any time.
Notation and units
The picture
| Symbol | Meaning |
|---|---|
| The full time-dependent wavefunction | |
| The spatial part (solution of the stationary equation) | |
| An operator (hatted); is the corresponding classical quantity or eigenvalue | |
| Expectation value | |
| Standard deviation (some books write ) | |
| , | Dirac notation, used from chapter 3 onwards |
| , , | Euler’s number, the imaginary unit and the differential (upright) |
The mathematics
The prose always keeps and full dimensions, so that any formula can be checked by substituting SI or eV units directly.
The simulations work internally in natural units, , because then energies, lengths and times are all O(1): slider ranges are easy to choose and floating-point precision is comfortable. Converting back to SI is covered in appendix C.
Handy conversions (very useful for estimates):
State of the content
The site is under construction. The n/m after each chapter in the contents tree is “finalised sections / total sections”; sections marked “to write” currently have only an outline.
The one chapter written out in full is chapter 2, which also serves as the template for the rest: every section has a complete (collapsible) derivation, a picture-versus-formalism comparison, at least one interactive simulation (or an explicit statement of why there is none), a summary of key formulas and a quiz.
Where to start
- Never studied quantum mechanics → 1.1 The crisis of classical physics
- Studied it but want the intuition → 2.1 The probability interpretation of the wavefunction
- Only want something that runs → go straight to 2.11 Tunnelling and drag the barrier width around
Section 1 of 106 · use ← → to turn the page