Quantum Tunneling — WKB Barrier Penetration
Wentzel-Kramers-Brillouin approximation: T ≈ exp(−2∫√(2m(V−E))/ℏ dx)
Particle
Energy E:
0.40
(V₀=1)
Mass m:
1.0
Barrier
Height V₀:
1.0
Width a:
1.5
Shape:
Rectangular
Gaussian
Triangular
Double barrier
Animate Wavepacket
T = —
WKB tunneling:
T=exp(−2γ) where γ=∫√(2m(V(x)−E))/ℏ dx over classically forbidden region. Exact for E<V₀. Resonance (T=1) at E>V₀ for double barriers (Fabry-Pérot). Applications: α-decay, scanning tunneling microscopy, Josephson junctions.