Quantum Tunneling

1D Schrodinger equation — Gaussian wavepacket meets a potential barrier

Transmission: — | Reflection: —
A quantum particle (wavepacket) approaches a rectangular potential barrier. If energy < barrier height, classical physics says "reflected 100%". But quantum mechanics allows tunneling — the wavefunction leaks through. Watch the probability density |ψ|² split at the barrier. This underlies scanning tunneling microscopes, nuclear fusion in stars, and transistors.