QUANTUM TUNNELING — WKB Semiclassical Barrier Transmission

2.0
2.0
1.00
0.25
T = — | WKB: T ≈ —
WAVEFUNCTION |ψ|² + potential V(x)
TRANSMISSION T(E) vs ENERGY
WKB INTEGRAND κ(x) in barrier
WKB approximation: T ≈ exp(−2∫κ(x)dx) where κ(x)=√(2m(V(x)−E))/ℏ is the decay constant. Above barrier: oscillatory wavefunction, T can reach 1 (resonance). Below barrier: exponential decay, quantum tunneling. Exact T from transfer matrix shown in comparison.