Quantum Tunneling — WKB Barrier

1D Gaussian wave packet incident on a rectangular potential barrier — split-operator time evolution

Tunneling T: 0.000 Reflection R: 0.000 WKB prediction: - Norm: 1.000
About: A quantum particle described by a Gaussian wave packet encounters a rectangular potential barrier. The time-dependent Schrödinger equation is evolved using a simplified finite-difference scheme. The WKB approximation predicts tunneling probability T ≈ exp(−2∫√(2m(V−E))dx/ℏ). Even when E < V₀, the wave function leaks through — a purely quantum effect with no classical analog, underlying phenomena from alpha decay to scanning tunneling microscopy.