A simulation of the time-dependent Schrödinger equation in 2D.
The core concept of Quantum Mechanics is that particles, like electrons, behave like waves described by a wavefunction $\psi(x,t)$.
This simulation solves:
In classical physics, a ball cannot roll over a hill if it doesn't have enough energy. In quantum mechanics, the wave can "leak" through the barrier.
This is how flash memory works, how alpha decay happens, and even how the sun shines (proton-proton fusion).
Brightness = Probability Density $|\psi|^2$ (Where the particle is effectively).
Color = Phase (The complex angle of $\psi$). The rainbow colors indicate the momentum/flow.
White Areas = Potential Barriers $V(x)$.