Quantum Tunneling Through Barrier

1D Schrödinger: wave packet tunneling, T = |t|², WKB, resonant tunneling

T = — | R = — | κL = —

Barrier V₀: 5.0
Barrier width L: 0.8
E (wave energy): 3.0
Mode:

Quantum tunneling occurs because the wavefunction decays exponentially as ψ ∝ e^(−κx) inside a classically forbidden region with κ = √(2m(V₀−E))/ℏ. The WKB transmission T ≈ e^(−2κL) for thick barriers. In a double-barrier system, resonant tunneling occurs when the energy matches a quasi-bound state (T → 1), the principle behind resonant tunneling diodes (RTDs) used in THz oscillators.