How to use it
Press Fire packets. A wave packet rolls in from the left at energy E and meets a barrier of height V₀. Classically, if E < V₀ it must bounce. Quantum-mechanically a sliver leaks through: that's the small packet on the right. Widen the barrier or switch to a heavier particle and watch T collapse.
What you're actually seeing
This is a live solution of the time-dependent Schrödinger equation (split-step method): the cyan curve is the real evolving |ψ|². The amber block is the barrier; the gold dashed line is the energy E. Inside the barrier the wave doesn't oscillate. It decays, by e⁻¹ every 1/κ. The bottom graph is the exact transmission T(E).
Why it runs the universe
Tunnelling isn't exotic. It's load-bearing. The Sun only fuses because protons tunnel their mutual repulsion. Alpha decay is an alpha particle tunnelling out of a nucleus (Gamow, 1928). The STM images single atoms because the tunnelling current changes ~10× per ångström. Flash memory stores bits by tunnelling electrons through an oxide.
What's exact, what's stylised
Exact: the transmission formula T(E), the decay constant κ = √(2m(V₀−E))/ℏ, the real per-particle numbers, and the Schrödinger evolution itself. Stylised: the barrier is an idealised rectangle (real ones, Coulomb or oxide, are shaped), the animation uses scaled units, and the packet width and speed are dialled for watchability.