Quantum Tunneling
In classical mechanics, a particle encountering a potential barrier higher than its kinetic energy is simply reflected — it cannot pass. Quantum mechanics tells a profoundly different story. The particle's wave function penetrates into the classically forbidden region, decaying exponentially but never reaching exactly zero. If the barrier is thin enough, a portion of the wave function emerges on the other side, giving a non-zero probability of transmission.
The Rectangular Barrier Model
This simulator models the simplest tunneling scenario: a particle of energy E approaching a rectangular potential barrier of height V and width L. When E < V, the wave function inside the barrier takes the form psi ~ exp(-kappa x), where kappa = sqrt(2m(V-E))/hbar is the decay constant. The transmission coefficient T quantifies the fraction of incident flux that passes through.
Exponential Sensitivity
The key insight is that tunneling probability depends exponentially on both barrier width and the energy deficit (V-E). Doubling the barrier width squares the suppression factor. This exponential sensitivity is why tunneling is significant at the atomic scale (barriers ~nm wide) but utterly negligible for macroscopic objects.
Physical Applications
Quantum tunneling powers some of the most important processes in nature and technology. Nuclear fusion in stellar cores requires protons to tunnel through the Coulomb barrier. Alpha decay is explained by the alpha particle tunneling out of the nuclear potential well — Gamow's 1928 theory was one of the first triumphs of quantum mechanics. In technology, the scanning tunneling microscope (STM) exploits the exponential sensitivity of tunneling current to image surfaces at atomic resolution.
Reading the Visualization
The red shaded rectangle is the potential barrier. The cyan wave on the left is the incoming particle's wave function, oscillating with wavelength determined by its energy. Inside the barrier, the wave decays exponentially. On the right, the transmitted wave continues with reduced amplitude (proportional to sqrt(T)). Adjust energy toward the barrier height to see tunneling increase dramatically — and above V, watch it become full transmission with oscillatory resonance effects.