Quantum mechanics attracts more nonsense than any other part of physics, mostly because the honest version is hard to picture and the dishonest version is easy. So this page does only what it can compute exactly. Every number below comes from a standard formula evaluated here in your browser and checked against published values — the electron in a 1 nm box really does sit at 0.376 eV, and the barrier really does transmit 2.4% of the electrons you throw at it.
Electrons arrive at the screen one at a time, and each lands in a place you cannot predict. Fire enough of them and a striped pattern appears that no single electron could have made — the stripes are a property of the distribution, and each electron is drawn from it. Close one slit and the stripes vanish, because a wave that only went through one opening has nothing to interfere with.
Trap an electron between two walls and only certain wavelengths fit — the same reason a guitar string has particular notes and not the ones in between. That is the whole origin of "quantised" energy: not a rule imposed on nature, but what happens to any wave you confine. Notice the lowest level is not zero. A trapped particle cannot be still, because being still would mean knowing both where it is and that it is not moving.
Send an electron at a barrier taller than its energy. Classically nothing gets through, ever. The wave does not stop at the wall — it decays inside it, and if the wall is thin enough there is still something left on the far side. The transmitted fraction falls off exponentially with thickness, which is why widening the barrier from 0.5 to 1.0 nm below drops transmission by a factor of 166, and why a scanning tunnelling microscope can feel a single atom of extra height.
A wave with one exact wavelength goes on forever — it is nowhere in particular. To build something localised you have to add together many wavelengths, and the tighter you want the packet, the wider the range of wavelengths you need. Momentum is wavelength, so this is not a limit on your instruments. It is a statement about what a wave can be. Drag the slider and watch the product refuse to go below ħ/2.
Everything has a wavelength — h divided by its momentum. For anything you can see, that wavelength is so much smaller than the object itself that no wave behaviour is observable, even in principle. The table is the whole reason the world looks classical.
| object | momentum | de Broglie wavelength | compared to its own size |
|---|
The interference pattern is the standard two-slit intensity — a cos² fringe term times a sinc² single-slit envelope — and each detection is a real random draw from that distribution, not a dot placed on a curve. Energy levels use En = n²h²/8mL², which gives 0.376 eV for n = 1 in a 1 nm box and 37.6 eV in a 0.1 nm box, both matching published figures. Tunnelling uses the exact rectangular-barrier transmission coefficient and returns 2.355 × 10⁻² for a 1 eV electron on a 2 eV, 0.5 nm barrier, against a textbook value of about 2.4 × 10⁻². The uncertainty product is measured from the packet by numerical integration rather than asserted, and a Gaussian comes out at ħ/2 to four decimal places.
What this leaves out is most of the subject. There is no time evolution, no spin, no entanglement, and no attempt to say what a measurement is — that last one is a live argument among physicists, not a settled fact being simplified for you. The barrier here is a perfect rectangle, real ones are not, and the box has infinitely high walls, which nothing does. These are the standard teaching idealisations; they get the physics right and the engineering approximately.