Imagine you could shrink until a row of atoms looked like stepping stones. An electron isn't a tiny marble hopping between them. It is a quantum wave, and the brighter a stone glows, the more of that wave lives there.
Each bump tells you where the neighborhood has available quantum songs. Tap a dot below to hear a different one, visually.
Scientific notebook: The data are numerically diagonalized eigenvalues and eigenvectors of a 12-site, one-orbital, open-boundary tight-binding Hamiltonian H = Σ εᵢ|i⟩⟨i| − Σ(|i⟩⟨i+1| + h.c.). Regular εᵢ=0; alternating εᵢ=±0.65; disordered εᵢ drawn once with seed 47 in [−1.8,1.8]. Density of states is Gaussian broadened (σ=0.15). IPR=Σᵢ|ψᵢ|⁴. This is an honest quantum teaching model, NOT the full A7 bismuth/Pb–Bi/Mg–Zn Hamiltonian or a reproduction of the supplied scientific graph. It runs without internet access.