Particle energy E (eV)
3.00
Barrier height V₀ (eV)
5.00
Barrier width d (Å)
2.00
Barrier shape
T = —
ln(T) = —
κ₀ = — Å⁻¹
∫κdx = —
ln(T) = —
κ₀ = — Å⁻¹
∫κdx = —
WKB Approximation
For E < V(x), the wavefunction decays as:
ψ ∝ exp(−∫κ(x)dx)
κ(x) = √[2m(V(x)−E)] / ℏ
Transmission: T = exp(−2∫κ dx)
Applications: alpha decay (Gamow 1928), scanning tunneling microscope, Josephson junctions, nuclear fusion in stars.
For E < V(x), the wavefunction decays as:
ψ ∝ exp(−∫κ(x)dx)
κ(x) = √[2m(V(x)−E)] / ℏ
Transmission: T = exp(−2∫κ dx)
Applications: alpha decay (Gamow 1928), scanning tunneling microscope, Josephson junctions, nuclear fusion in stars.