Airy Functions & WKB Quantum Tunneling
Exact Airy solution near turning points; WKB approximation in classically allowed/forbidden regions
Wavefunction ψ(x)
Potential V(x)
Energy E
Energy E
0.40
Barrier Width
20
Barrier Height
0.70
ℏ (effective)
0.12
WKB tunneling amplitude T ≈ exp(−2∫√(2m(V−E)/ℏ²) dx) | Airy Ai(z) exact at turning points