Editing Quantum tunnelling (section)

== History ==
The Schrödinger equation was published in 1926. The first person to apply the Schrödinger equation to a problem that involved tunneling between two classically allowed regions through a potential barrier was [[Friedrich Hund]] in a series of articles published in 1927. He studied the solutions of a [[double-well potential]] and discussed [[molecular spectra]].<ref name=":0">{{cite journal |last1=Merzbacher |first1=Eugen |title=The Early History of Quantum Tunneling |url=https://physicstoday.scitation.org/doi/10.1063/1.1510281 |journal=Physics Today |access-date=17 August 2022 |date=August 2002 |volume=55 |issue=8 |pages=44–49 |doi=10.1063/1.1510281 |bibcode=2002PhT....55h..44M |quote=Friedrich Hund ... was the first to make use of quantum mechanical barrier penetration ...}}</ref> [[Leonid Mandelstam]] and [[Mikhail Leontovich]] discovered tunneling independently and published their results in 1928.<ref>{{cite journal |first1=L. |last1=Mandelstam |first2=M. |last2=Leontowitsch |title=Zur Theorie der Schrödingerschen Gleichung |journal=Zeitschrift für Physik |volume=47 |issue= 1–2|pages=131–136 |year=1928 |bibcode = 1928ZPhy...47..131M |doi = 10.1007/BF01391061 |s2cid=125101370 }}</ref>

In 1927, [[Lothar Wolfgang Nordheim|Lothar Nordheim]], assisted by [[Ralph H. Fowler|Ralph Fowler]], published a paper that discussed [[thermionic emission]] and reflection of electrons from metals. He assumed a surface potential barrier that confines the electrons within the metal and showed that the electrons have a finite probability of tunneling through or reflecting from the surface barrier when their energies are close to the barrier energy. Classically, the electron would either transmit or reflect with 100% certainty, depending on its energy. In 1928 [[J. Robert Oppenheimer]] published two papers on [[field emission]], ''i.e.'' the emission of electrons induced by strong electric fields. Nordheim and Fowler simplified Oppenheimer's derivation and found values for the emitted currents and [[work function]]s that agreed with experiments.<ref name=":0" />

A great success of the tunnelling theory was the mathematical explanation for [[alpha decay]], which was developed in 1928 by [[George Gamow]] and independently by [[Ronald Wilfred Gurney|Ronald Gurney]] and [[Edward Condon]].<ref>{{cite journal |first1=R. W. |last1=Gurney |first2=E. U. |last2=Condon |title=Quantum Mechanics and Radioactive Disintegration |journal=Nature |volume=122 |issue= 3073|pages=439 |year=1928 |bibcode = 1928Natur.122..439G |doi = 10.1038/122439a0 |s2cid=4090561 |doi-access=free }}</ref><ref>{{cite journal |last1=Gurney |first1=R. W. |last2=Condon |first2=E. U. |year=1929 |title=Quantum Mechanics and Radioactive Disintegration |journal=Physical Review |volume=33 |issue=2 |pages=127–140 |bibcode=1929PhRv...33..127G |doi=10.1103/PhysRev.33.127}}</ref><ref>{{cite interview |last=Bethe |first=Hans |subject-link=Hans Bethe |interviewer=Charles Weiner |title=Hans Bethe – Session I |url=https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4504-1 |access-date=1 May 2016 |work=Niels Bohr Library & Archives, American Institute of Physics, College Park, Maryland, USA |place=Cornell University |date=27 October 1966 |interviewer2=[[Jagdish Mehra]]}}</ref><ref name="Nuc&RadChem">{{cite book| last1=Friedlander |first1=Gerhart |last2=Kennedy |first2=Joseph E. |last3=Miller |first3=Julian Malcolm |title=Nuclear and Radiochemistry | url=https://archive.org/details/nuclearradiochem00frie | url-access=registration |edition=2nd |year=1964 |publisher=John Wiley & Sons |location=New York | isbn=978-0-471-86255-0 | pages=[https://archive.org/details/nuclearradiochem00frie/page/225 225–7]}}</ref> The latter researchers simultaneously solved the Schrödinger equation for a model nuclear potential and derived a relationship between the [[half-life]] of the particle and the energy of emission that depended directly on the mathematical probability of tunneling. All three researchers were familiar with the works on field emission,<ref name=":0" /> and Gamow was aware of Mandelstam and Leontovich's findings.<ref>{{cite journal |last=Feinberg |first=E. L. |year=2002 |title=The forefather (about Leonid Isaakovich Mandelstam) |journal=Physics-Uspekhi |volume=45 |issue=1 |pages=81–100 |bibcode=2002PhyU...45...81F |doi=10.1070/PU2002v045n01ABEH001126 |s2cid=250780246}}</ref>

In the early days of quantum theory, the term ''tunnel effect'' was not used, and the effect was instead referred to as penetration of, or leaking through, a barrier. The German term ''wellenmechanische Tunneleffekt'' was used in 1931 by Walter Schottky.<ref name=":0" /> The English term ''tunnel effect'' entered the language in 1932 when it was used by Yakov Frenkel in his textbook.<ref name=":0" />

In 1957 [[Leo Esaki]] demonstrated tunneling of electrons over a few nanometer wide barrier in a [[semiconductor]] structure and developed a [[diode]] based on tunnel effect.<ref>{{Cite journal |last=Esaki |first=Leo |date=1974-03-22 |title=Long Journey into Tunneling |url=https://www.science.org/doi/10.1126/science.183.4130.1149 |journal=Science |language=en |volume=183 |issue=4130 |pages=1149–1155 |doi=10.1126/science.183.4130.1149 |pmid=17789212 |bibcode=1974Sci...183.1149E |s2cid=44642243 |issn=0036-8075}}</ref> In 1960, following Esaki's work, [[Ivar Giaever]] showed experimentally that tunnelling also took place in [[Superconductivity|superconductors]]. The tunnelling spectrum gave direct evidence of the [[superconducting energy gap]]. In 1962, [[Brian Josephson]] predicted the tunneling of superconducting [[Cooper pair]]s. Esaki, Giaever and Josephson shared the 1973 [[Nobel Prize in Physics]] for their works on quantum tunneling in solids.<ref>{{Cite book |last=Dardo |first=M. (Mauro) |url=http://archive.org/details/nobellaureatestw0000dard |title=Nobel laureates and twentieth-century physics |date=2004 |publisher=Cambridge, UK; New York : Cambridge University Press |others=Internet Archive |isbn=978-0-521-83247-2}}</ref><ref name="Razavy" />

In 1981, [[Gerd Binnig]] and [[Heinrich Rohrer]] developed a new type of microscope, called [[scanning tunneling microscope]], which is based on tunnelling and is used for imaging [[surface]]s at the [[atom]]ic level. Binnig and Rohrer were awarded the Nobel Prize in Physics in 1986 for their discovery.<ref>{{Cite journal |last1=Binnig |first1=Gerd |last2=Rohrer |first2=Heinrich |date=July 1987 |title=Scanning tunneling microscopy—from birth to adolescence |journal=Reviews of Modern Physics |language=en |volume=59 |issue=3 |pages=615–625 |bibcode=1987RvMP...59..615B |doi=10.1103/RevModPhys.59.615 |issn=0034-6861 |doi-access=free}}</ref>