Quantum Tunneling: How Particles Walk Through Walls — and Power the Sun

The Particle That Goes Through the Wall

Classical physics is straightforward about energy barriers. If a ball does not have enough kinetic energy to roll over a hill, it rolls back. No exceptions, no nuance. A particle on one side of a potential energy barrier — with less energy than the barrier height — simply cannot cross to the other side. Period.

Quantum mechanics is more complicated, and more interesting. Because quantum particles are described by wave functions that spread continuously through space, there is always a small but non-zero amplitude for the wave function to extend into and through a classically forbidden region. If the barrier is not infinitely wide or infinitely tall, the wave function can emerge on the other side with a small but non-zero amplitude — meaning the particle has a non-zero probability of being detected there. This is quantum tunneling.

Tunneling is not a particle "borrowing" energy to get over a barrier. The particle does not have enough energy to surmount the barrier classically, and it does not acquire that energy transiently. Instead, it transitions through a quantum state that has no classical analog. The wave function penetrates the barrier exponentially — the probability of emerging on the far side falls off rapidly with the barrier's width and height — but it never reaches exactly zero unless the barrier is infinitely thick.

The Sun Cannot Shine Without It

The most consequential application of quantum tunneling in nature is nuclear fusion. For two hydrogen nuclei (protons) to fuse, they must approach each other close enough for the strong nuclear force to engage — a distance of roughly one femtometer. But protons are both positively charged, and the electrostatic repulsion between them grows rapidly as they approach, creating a potential energy barrier called the Coulomb barrier.

Calculations show that the temperature at the Sun's core — about 15 million kelvin — is not actually high enough to give protons sufficient kinetic energy to classically overcome the Coulomb barrier. Protons moving at the thermal speeds corresponding to 15 million kelvin would be stopped well before reaching fusion distance in classical physics. What makes fusion happen is that the protons tunnel through the barrier. Their wave functions have a small but non-zero amplitude on the far side of the Coulomb barrier, and over the vast number of proton-proton collisions occurring every second in the Sun's core, a small fraction succeed by tunneling. Without quantum tunneling, the Sun would not shine, and Earth would be dark and frozen.

Radioactive Decay and Alpha Emission

Quantum tunneling also explains alpha decay — the process by which certain heavy atomic nuclei emit a helium-4 nucleus (an alpha particle). The alpha particle exists as a quantum object inside the nucleus but is bound by the nuclear force that creates a potential barrier at the nuclear surface. Classically, the alpha particle does not have enough energy to escape over this barrier. Quantum mechanically, it continuously tunnels against the barrier, and eventually, after a characteristic waiting time that varies from microseconds to billions of years depending on the specific nucleus, it tunnels through and escapes.

George Gamow explained alpha decay in terms of tunneling in 1928, one of the first successful applications of quantum mechanics to nuclear physics.

Tunneling in Technology

Quantum tunneling is not only an astrophysical phenomenon — it is engineered into the devices you use every day. Tunnel diodes exploit controlled tunneling of electrons through thin semiconductor barriers to achieve very fast switching. The scanning tunneling microscope, invented in 1981, works by measuring the tunneling current between a sharp metallic tip and a surface as a function of position, achieving resolution sufficient to image individual atoms. Flash memory — the storage technology in smartphones and solid-state drives — stores data by manipulating the tunneling of electrons through thin oxide layers in transistors. The quantum world is not distant and esoteric; it is operational inside every digital device in existence.