Quantum tunneling in the context of Quantum indeterminacy

A scanning tunneling microscope (STM) is a type of scanning probe microscope used for imaging surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer, then at IBM Zürich, the Nobel Prize in Physics in 1986. STM senses the surface by using an extremely sharp conducting tip that can distinguish features smaller than 0.1 nm with a 0.01 nm (10 pm) depth resolution. This means that individual atoms can routinely be imaged and manipulated. Most scanning tunneling microscopes are built for use in ultra-high vacuum at temperatures approaching absolute zero, but variants exist for studies in air, water and other environments, and for temperatures over 1000 °C.

STM is based on the concept of quantum tunneling. When the tip is brought very near to the surface to be examined, a bias voltage applied between the two allows electrons to tunnel through the vacuum separating them. The resulting tunneling current is a function of the tip position, applied voltage, and the local density of states (LDOS) of the sample. Information is acquired by monitoring the current as the tip scans across the surface, and is usually displayed in image form.

Ivar Giaever (/ˈjeɪvər/ YAY-ver; Norwegian: Ivar Giæver, pronounced [ˈîːvɑr ˈjæːvər]; April 5, 1929 – June 20, 2025) was a Norwegian–American experimental physicist who shared the 1973 Nobel Prize in Physics with Leo Esaki and Brian Josephson. One half of the prize was jointly awarded to Esaki and Giaever "for their experimental discoveries regarding tunneling phenomena in semiconductors and superconductors, respectively."

George Gamow (sometimes Gammoff; born Georgiy Antonovich Gamov; Russian: Гео́ргий Анто́нович Га́мов; March 4 [O.S. February 20] 1904 – August 19, 1968) was a Soviet and American polymath, theoretical physicist and cosmologist. He was an early advocate and developer of Georges Lemaître's Big Bang theory. Gamow discovered a theoretical explanation of alpha decay by quantum tunneling, invented the liquid drop model (the first mathematical model of the atomic nucleus), worked on radioactive decay, star formation, stellar nucleosynthesis, Big Bang nucleosynthesis (which he collectively called nucleocosmogenesis), and predicted the existence of the cosmic microwave background radiation and molecular genetics. Gamow was a key figure in the development and understanding of quantum tunneling.

In his middle and late career, Gamow directed much of his attention to teaching and wrote popular books on science, including One Two Three... Infinity and the Mr Tompkins series of books (1939–1967). Some of his books remain in print more than a half-century after their original publication. The George Gamow Memorial Lectures at the University of Colorado at Boulder are given in his honor.

In quantum mechanics, the rectangular (or, at times, square) potential barrier is a standard one-dimensional problem that demonstrates the phenomena of wave-mechanical tunneling (also called "quantum tunneling") and wave-mechanical reflection. The problem consists of solving the one-dimensional time-independent Schrödinger equation for a particle encountering a rectangular potential energy barrier. It is usually assumed, as here, that a free particle impinges on the barrier from the left.

Although classically a particle behaving as a point mass would be reflected if its energy is less than ${\displaystyle V_{0}}$, a particle actually behaving as a matter wave has a non-zero probability of penetrating the barrier and continuing its travel as a wave on the other side. In classical wave-physics, this effect is known as evanescent wave coupling. The likelihood that the particle will pass through the barrier is given by the transmission coefficient, whereas the likelihood that it is reflected is given by the reflection coefficient. Schrödinger's wave-equation allows these coefficients to be calculated.