quantum tunneling

History

The phenomenon was first described in 1928 when George Gamow explained alpha decay of radioactive nuclei. Later, tunneling became key to semiconductor electronics (tunnel diodes) and explaining nuclear fusion in stars.

How it works

An electron in a transistor encounters an energy barrier, but due to its wave nature, it can 'seep' through, creating a tunnel current. This resembles water seeping through sand, though the sand seems like a solid barrier.

History

The phenomenon was first described in 1928 when George Gamow explained alpha decay of radioactive nuclei. Later, tunneling became key to semiconductor electronics (tunnel diodes) and explaining nuclear fusion in stars.

How it works

An electron in a transistor encounters an energy barrier, but due to its wave nature, it can 'seep' through, creating a tunnel current. This resembles water seeping through sand, though the sand seems like a solid barrier.

History

The first theoretical explanation of tunneling was given in 1928 independently by George Gamow, and also by Ronald Gurney and Edward Condon for alpha decay of nuclei. Subsequently, the phenomenon was applied in solid-state physics: Leo Esaki in 1958 created the tunnel diode, for which he received the Nobel Prize. In astrophysics, tunneling explained the mechanism of stellar nucleosynthesis (Hans Bethe, 1938). Later, Stephen Hawking used the concept of tunneling to describe black hole radiation.

How it works

Within nonrelativistic quantum mechanics, tunneling is described by solving the stationary Schrödinger equation for a potential with a barrier. The wavefunction inside the barrier (E < V₀) has the form ψ(x) ∝ e^{-κx}, where κ = √(2m(V₀−E))/ħ. The transmission coefficient (tunneling probability) for a rectangular barrier of width L: T ≈ e^{-2κL}. The Heisenberg uncertainty principle allows a temporary violation of energy conservation, making tunneling possible. This effect is also used to explain the cosmological birth of the Universe and Hawking radiation.

Open problems & fun facts

Tunneling time: how much time does a particle spend in the classically forbidden region? The Hartman paradox points to the possibility of superluminal tunneling.; Macroscopic tunneling: is quantum tunneling possible for systems with a large number of particles?; Precise description of tunneling in complex systems with dissipation and interaction with the environment.

💡 Without quantum tunneling, the Sun wouldn't shine: hydrogen nuclei overcome mutual repulsion and fuse only thanks to the tunnel effect.