Quantum Tunnelling: Passing Through a Barrier You Cannot Climb

**Quantum tunnelling** is the phenomenon in which a particle passes through a potential barrier that, classically, it lacks the energy to surmount. ## Why it happens In quantum mechanics a particle is described by a wavefunction, and the wavefunction does not stop abruptly at a barrier — it decays exponentially inside it. If the barrier is thin enough, the amplitude on the far side is non-zero, so there is a finite probability of finding the particle there. Nothing is "borrowed" and no energy conservation is violated. The particle does not acquire energy to climb the barrier; it was never localised in the classical sense to begin with. For a rectangular barrier the transmission probability is approximately T ≈ exp(−2κd), κ = √(2m(V − E))/ℏ with *d* the barrier width, *m* the particle mass, and *V − E* the height above the particle's energy. The **exponential dependence on width and on the square root of mass** is the single most important feature: doubling the width squares the suppression, and heavier particles tunnel exponentially less. It is why tunnelling dominates for electrons, is marginal for hydrogen, and is irrelevant for anything larger. ## Where it matters - **Nuclear fusion in stars.** Protons cannot classically overcome mutual repulsion at solar core temperatures. The Sun shines because they tunnel. - **Alpha Decay: Gamow's 1928 Tunnelling Explanation** — the first successful quantum explanation of a nuclear process. - **Semiconductor devices.** Tunnel diodes exploit it deliberately; leakage through gate oxides is a limit on transistor scaling, and charge tunnelling on and off floating gates is how NAND Flash Memory: How Solid-State Storage Stores Data in Trapped Electrons works — and how it eventually loses data. - **Scanning tunnelling microscopy.** Tunnelling current between tip and surface varies so sharply with distance that individual atoms are resolvable. - **Biochemistry.** Electron and proton tunnelling participate in enzyme catalysis and in the The Electron Transport Chain: The Mitochondrial Assembly Line That Makes Most of Your ATP. ## Scale limits Tunnelling is not restricted to elementary particles — matter-wave experiments have demonstrated quantum behaviour for progressively more massive molecules and clusters. But the exponential mass dependence means the effect vanishes rapidly with size, which is why macroscopic tunnelling is a thought experiment rather than a phenomenon. See Can You Tunnel Through the Floor? The Compound Probability and the Barrier Maths.