Quantum Tunnelling

A Gaussian wavepacket evolving under the time-dependent Schrodinger equation, solved by Crank-Nicolson so the total probability is conserved to round-off at every step. The terrain is the potential V(x); the luminous curtain is the probability density, coloured by the quantum phase. A classical ball with the same mean energy is launched alongside: it always reflects off a barrier taller than its energy, while the quantum packet partly tunnels through. Raise, widen and sculpt the barrier and watch the transmitted fraction change; the resonant double barrier transmits almost perfectly at special energies.