The **history of quantum mechanics ** is a fundamental part of the history of modern physics. Quantum mechanics' history, as it interlaces with the history of quantum chemistry, began essentially with a number of different scientific discoveries: the 1838 discovery of cathode rays by Michael Faraday; the 1859–60 winter statement of the black-body radiation problem by Gustav Kirchhoff; the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system could be *discrete*; the discovery of the photoelectric effect by Heinrich Hertz in 1887; and the 1900 quantum hypothesis by Max Planck that any energy-radiating atomic system can theoretically be divided into a number of discrete "energy elements" *ε* (Greek letter epsilon) such that each of these energy elements is proportional to the frequency *ν* with which each of them individually radiate energy, as defined by the following formula:

where *h* is a numerical value called Planck's constant.

Then, Albert Einstein in 1905, in order to explain the photoelectric effect previously reported by Heinrich Hertz in 1887, postulated consistently with Max Planck's quantum hypothesis that light itself is made of individual quantum particles, which in 1926 came to be called photons by Gilbert N. Lewis. The photoelectric effect was observed upon shining light of particular wavelengths on certain materials, such as metals, which caused electrons to be ejected from those materials only if the light quantum energy was greater than the work function of the metal's surface.

The phrase "quantum mechanics" was coined (in German, *Quantenmechanik*) by the group of physicists including Max Born, Werner Heisenberg, and Wolfgang Pauli, at the University of Göttingen in the early 1920s, and was first used in Born's 1924 paper *"Zur Quantenmechanik"*.^{ [1] } In the years to follow, this theoretical basis slowly began to be applied to chemical structure, reactivity, and bonding.

Ludwig Boltzmann suggested in 1877 that the energy levels of a physical system, such as a molecule, could be discrete (as opposed to continuous). He was a founder of the Austrian Mathematical Society, together with the mathematicians Gustav von Escherich and Emil Müller. Boltzmann's rationale for the presence of discrete energy levels in molecules such as those of iodine gas had its origins in his statistical thermodynamics and statistical mechanics theories and was backed up by mathematical arguments, as would also be the case twenty years later with the first quantum theory put forward by Max Planck.

In 1900, the German physicist Max Planck reluctantly introduced the idea that energy is *quantized* in order to derive a formula for the observed frequency dependence of the energy emitted by a black body, called Planck's law, that included a Boltzmann distribution (applicable in the classical limit). Planck's law^{ [2] } can be stated as follows: where:

*I*(*ν*,*T*) is the energy per unit time (or the power) radiated per unit area of emitting surface in the normal direction per unit solid angle per unit frequency by a black body at temperature*T*;*h*is the Planck constant;*c*is the speed of light in a vacuum;*k*is the Boltzmann constant;*ν*(nu) is the frequency of the electromagnetic radiation; and*T*is the temperature of the body in kelvins.

The earlier Wien approximation may be derived from Planck's law by assuming .

Moreover, the application of Planck's quantum theory to the electron allowed Ștefan Procopiu in 1911–1913, and subsequently Niels Bohr in 1913, to calculate the magnetic moment of the electron, which was later called the "magneton;" similar quantum computations, but with numerically quite different values, were subsequently made possible for both the magnetic moments of the proton and the neutron that are three orders of magnitude smaller than that of the electron.

Photoelectric effect | |

The photoelectric effect reported by Heinrich Hertz in 1887, | |

and explained by Albert Einstein in 1905. | |

Low-energy phenomena: Photoelectric effect | |

Mid-energy phenomena: Compton scattering | |

High-energy phenomena: Pair production |

In 1905, Albert Einstein explained the photoelectric effect by postulating that light, or more generally all electromagnetic radiation, can be divided into a finite number of "energy quanta" that are localized points in space. From the introduction section of his March 1905 quantum paper, "On a heuristic viewpoint concerning the emission and transformation of light", Einstein states:

"According to the assumption to be contemplated here, when a light ray is spreading from a point, the energy is not distributed continuously over ever-increasing spaces, but consists of a finite number of 'energy quanta' that are localized in points in space, move without dividing, and can be absorbed or generated only as a whole."

This statement has been called the most revolutionary sentence written by a physicist of the twentieth century.^{ [3] } These *energy quanta* later came to be called "photons", a term introduced by Gilbert N. Lewis in 1926. The idea that each photon had to consist of energy in terms of quanta was a remarkable achievement; it effectively solved the problem of black-body radiation attaining infinite energy, which occurred in theory if light were to be explained only in terms of waves. In 1913, Bohr explained the spectral lines of the hydrogen atom, again by using quantization, in his paper of July 1913 *On the Constitution of Atoms and Molecules*.

These theories, though successful, were strictly phenomenological: during this time, there was no rigorous justification for quantization, aside, perhaps, from Henri Poincaré's discussion of Planck's theory in his 1912 paper *Sur la théorie des quanta*.^{ [4] }^{ [5] } They are collectively known as the * old quantum theory *.

The phrase "quantum physics" was first used in Johnston's *Planck's Universe in Light of Modern Physics* (1931).

In 1923, the French physicist Louis de Broglie put forward his theory of matter waves by stating that particles can exhibit wave characteristics and vice versa. This theory was for a single particle and derived from special relativity theory. Building on de Broglie's approach, modern quantum mechanics was born in 1925, when the German physicists Werner Heisenberg, Max Born, and Pascual Jordan ^{ [6] }^{ [7] } developed matrix mechanics and the Austrian physicist Erwin Schrödinger invented wave mechanics and the non-relativistic Schrödinger equation as an approximation of the generalised case of de Broglie's theory.^{ [8] } Schrödinger subsequently showed that the two approaches were equivalent.

Heisenberg formulated his uncertainty principle in 1927, and the Copenhagen interpretation started to take shape at about the same time. Starting around 1927, Paul Dirac began the process of unifying quantum mechanics with special relativity by proposing the Dirac equation for the electron. The Dirac equation achieves the relativistic description of the wavefunction of an electron that Schrödinger failed to obtain. It predicts electron spin and led Dirac to predict the existence of the positron. He also pioneered the use of operator theory, including the influential bra–ket notation, as described in his famous 1930 textbook. During the same period, Hungarian polymath John von Neumann formulated the rigorous mathematical basis for quantum mechanics as the theory of linear operators on Hilbert spaces, as described in his likewise famous 1932 textbook. These, like many other works from the founding period, still stand, and remain widely used.

The field of quantum chemistry was pioneered by physicists Walter Heitler and Fritz London, who published a study of the covalent bond of the hydrogen molecule in 1927. Quantum chemistry was subsequently developed by a large number of workers, including the American theoretical chemist Linus Pauling at Caltech, and John C. Slater into various theories such as Molecular Orbital Theory or Valence Theory.

Beginning in 1927, researchers attempted to apply quantum mechanics to fields instead of single particles, resulting in quantum field theories. Early workers in this area include P.A.M. Dirac, W. Pauli, V. Weisskopf, and P. Jordan. This area of research culminated in the formulation of quantum electrodynamics by R.P. Feynman, F. Dyson, J. Schwinger, and S. Tomonaga during the 1940s. Quantum electrodynamics describes a quantum theory of electrons, positrons, and the electromagnetic field, and served as a model for subsequent quantum field theories.^{ [6] }^{ [7] }^{ [9] }

The theory of quantum chromodynamics was formulated beginning in the early 1960s. The theory as we know it today was formulated by Politzer, Gross and Wilczek in 1975.

Building on pioneering work by Schwinger, Higgs and Goldstone, the physicists Glashow, Weinberg and Salam independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single electroweak force, for which they received the 1979 Nobel Prize in Physics.

- Thomas Young's double-slit experiment demonstrating the wave nature of light. (c. 1801)
- Henri Becquerel discovers radioactivity. (1896)
- J. J. Thomson's cathode ray tube experiments (discovers the electron and its negative charge). (1897)
- The study of black-body radiation between 1850 and 1900, which could not be explained without quantum concepts.
- The photoelectric effect: Einstein explained this in 1905 (and later received a Nobel prize for it) using the concept of photons, particles of light with quantized energy.
- Robert Millikan's oil-drop experiment, which showed that electric charge occurs as
*quanta*(whole units). (1909) - Ernest Rutherford's gold foil experiment disproved the plum pudding model of the atom which suggested that the mass and positive charge of the atom are almost uniformly distributed. This led to the planetary model of the atom (1911).
- James Franck and Gustav Hertz's electron collision experiment shows that energy absorption by mercury atoms is quantized. (1914)
- Otto Stern and Walther Gerlach conduct the Stern–Gerlach experiment, which demonstrates the quantized nature of particle spin. (1920)
- Arthur Compton with Compton scattering experiment (1923)
- Clinton Davisson and Lester Germer demonstrate the wave nature of the electron
^{ [10] }in the electron diffraction experiment. (1927) - Carl David Anderson with the discovery positron (1932), validated Paul Dirac's theoretical prediction of this particle (1928)
- Lamb–Retherford experiment discovered Lamb shift (1947), which leaded to the development of quantum electrodynamics.
- Clyde L. Cowan and Frederick Reines confirm the existence of the neutrino in the neutrino experiment. (1955)
- Clauss Jönsson's double-slit experiment with electrons. (1961)
- The quantum Hall effect, discovered in 1980 by Klaus von Klitzing. The quantized version of the Hall effect has allowed for the definition of a new practical standard for electrical resistance and for an extremely precise independent determination of the fine structure constant.
- The experimental verification of quantum entanglement by John Clauser and Stuart Freedman. (1972)
- The Mach–Zehnder interferometer experiment conducted by Paul Kwiat, Harold Wienfurter, Thomas Herzog, Anton Zeilinger, and Mark Kasevich, providing experimental verification of the Elitzur–Vaidman bomb tester, proving interaction-free measurement is possible. (1994)

The **photon** is a type of elementary particle. It is the quantum of the electromagnetic field including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always move at the speed of light in vacuum, 299792458 m/s. The photon belongs to the class of bosons.

The **photoelectric effect** is the emission of electrons when electromagnetic radiation, such as light, hits a material. Electrons emitted in this manner are called photoelectrons. The phenomenon is studied in condensed matter physics, and solid state and quantum chemistry to draw inferences about the properties of atoms, molecules and solids. The effect has found use in electronic devices specialized for light detection and precisely timed electron emission.

**Quantum mechanics** is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.

**Quantum chemistry**, also called **molecular quantum mechanics**, is a branch of chemistry focused on the application of quantum mechanics to chemical systems. Understanding electronic structure and molecular dynamics using the Schrödinger equations are central topics in quantum chemistry.

**Wave–particle duality** is the concept in quantum mechanics that every particle or quantum entity may be described as either a particle or a wave. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the behaviour of quantum-scale objects. As Albert Einstein wrote:

It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.

**Louis Victor Pierre Raymond, 7th Duc de Broglie** was a French physicist and aristocrat who made groundbreaking contributions to quantum theory. In his 1924 PhD thesis, he postulated the wave nature of electrons and suggested that all matter has wave properties. This concept is known as the de Broglie hypothesis, an example of wave–particle duality, and forms a central part of the theory of quantum mechanics.

A timeline of atomic and subatomic physics.

**Matter waves** are a central part of the theory of quantum mechanics, being an example of wave–particle duality. All matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave. In most cases, however, the wavelength is too small to have a practical impact on day-to-day activities.

**Quantum optics** is a branch of atomic, molecular, and optical physics dealing with how individual quanta of light, known as photons, interact with atoms and molecules. It includes the study of the particle-like properties of photons. Photons have been used to test many of the counter-intuitive predictions of quantum mechanics, such as entanglement and teleportation, and are a useful resource for quantum information processing.

The **old quantum theory** is a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent, but was rather a set of heuristic corrections to classical mechanics. The theory is now understood as the semi-classical approximation to modern quantum mechanics.

The **Davisson–Germer experiment** was a 1923-27 experiment by Clinton Davisson and Lester Germer at Western Electric, in which electrons, scattered by the surface of a crystal of nickel metal, displayed a diffraction pattern. This confirmed the hypothesis, advanced by Louis de Broglie in 1924, of wave-particle duality, and was an experimental milestone in the creation of quantum mechanics.

The ** Annus mirabilis papers** are the four papers that Albert Einstein published in

**Quantum mechanics** is the study of very small things. It explains the behavior of matter and its interactions with energy on the scale of atomic and subatomic particles. By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the Moon. Classical physics is still used in much of modern science and technology. However, towards the end of the 19th century, scientists discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain. The desire to resolve inconsistencies between observed phenomena and classical theory led to two major revolutions in physics that created a shift in the original scientific paradigm: the *theory of relativity* and the development of *quantum mechanics*. This article describes how physicists discovered the limitations of classical physics and developed the main concepts of the quantum theory that replaced it in the early decades of the 20th century. It describes these concepts in roughly the order in which they were first discovered. For a more complete history of the subject, see *History of quantum mechanics*.

A **first quantization** of a physical system is a possibly semiclassical treatment of quantum mechanics, in which particles or physical objects are treated using quantum wave functions but the surrounding environment is treated classically.

This timeline lists significant discoveries in physics and the laws of nature, including experimental discoveries, theoretical proposals that were confirmed experimentally, and theories that have significantly influenced current thinking in modern physics. Such discoveries are often a multi-step, multi-person process. Multiple discovery sometimes occurs when multiple research groups discover the same phenomenon at about the same time, and scientific priority is often disputed. The listings below include some of the most significant people and ideas by date of publication or experiment.

The **Planck constant**, or **Planck's constant**, is a fundamental physical constant denoted , and is of fundamental importance in quantum mechanics. A photon's energy is equal to its frequency multiplied by the Planck constant. Due to mass–energy equivalence, the Planck constant also relates mass to frequency.

In physics, a **quantum** is the minimum amount of any physical entity involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum.

Physics is a scientific discipline that seeks to construct and experimentally test theories of the physical universe. These theories vary in their scope and can be organized into several distinct branches, which are outlined in this article.

The **timeline of quantum mechanics** is a list of key events in the history of quantum mechanics, quantum field theories and quantum chemistry.

In 1922, American physicist William Duane presented a discrete momentum-exchange model of the reflection of X-Ray photons by a crystal lattice. Duane showed that such a model gives the same scattering angles as the ones calculated via a wave diffraction model, see Bragg's Law.

- ↑ Max Born,
*My Life: Recollections of a Nobel Laureate*, Taylor & Francis, London, 1978. ("We became more and more convinced that a radical change of the foundations of physics was necessary, i.e., a new kind of mechanics for which we used the term quantum mechanics. This word appears for the first time in physical literature in a paper of mine...") - ↑ M. Planck (1914).
*The theory of heat radiation*, second edition, translated by M. Masius, Blakiston's Son & Co, Philadelphia, pp. 22, 26, 42–43. - ↑ Folsing, Albrecht (1997),
*Albert Einstein: A Biography*, trans. Ewald Osers, Viking - ↑ McCormmach, Russell (Spring 1967), "Henri Poincaré and the Quantum Theory",
*Isis*,**58**(1): 37–55, doi:10.1086/350182 - ↑ Irons, F. E. (August 2001), "Poincaré's 1911–12 proof of quantum discontinuity interpreted as applying to atoms",
*American Journal of Physics*,**69**(8): 879–84, Bibcode:2001AmJPh..69..879I, doi:10.1119/1.1356056 - 1 2 Edwards, David A. (1979). "The mathematical foundations of quantum mechanics".
*Synthese*. Springer Science and Business Media LLC.**42**(1): 1–70. doi:10.1007/bf00413704. ISSN 0039-7857. - 1 2 Edwards, David A. (1981). "Mathematical foundations of quantum field theory: Fermions, gauge fields, and supersymmetry part I: Lattice field theories".
*International Journal of Theoretical Physics*. Springer Science and Business Media LLC.**20**(7): 503–517. doi:10.1007/bf00669437. ISSN 0020-7748. - ↑ Hanle, P.A. (December 1977), "Erwin Schrodinger's Reaction to Louis de Broglie's Thesis on the Quantum Theory.",
*Isis*,**68**(4): 606–09, doi:10.1086/351880 - ↑ S. Auyang,
*How is Quantum Field Theory Possible?*, Oxford University Press, 1995. - ↑ The Davisson–Germer experiment, which demonstrates the wave nature of the electron

- Bacciagaluppi, Guido; Valentini, Antony (2009),
*Quantum theory at the crossroads: reconsidering the 1927 Solvay conference*, Cambridge, UK: Cambridge University Press, p. 9184, arXiv: quant-ph/0609184 , Bibcode:2006quant.ph..9184B, ISBN 978-0-521-81421-8, OCLC 227191829 - Bernstein, Jeremy (2009),
*Quantum Leaps*, Cambridge, Massachusetts: Belknap Press of Harvard University Press, ISBN 978-0-674-03541-6 - Cramer, JG (2015).
*The Quantum Handshake: Entanglement, Nonlocality and Transactions*. Springer Verlag. ISBN 978-3-319-24642-0. - Greenberger, Daniel, Hentschel, Klaus, Weinert, Friedel (Eds.)
*Compendium of Quantum Physics. Concepts, Experiments, History and Philosophy*, New York: Springer, 2009. ISBN 978-3-540-70626-7. - Jammer, Max (1966),
*The conceptual development of quantum mechanics*, New York: McGraw-Hill, OCLC 534562 - Jammer, Max (1974),
*The philosophy of quantum mechanics: The interpretations of quantum mechanics in historical perspective*, New York: Wiley, ISBN 0-471-43958-4, OCLC 969760 - F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization I,and II,
*Ann. Phys. (N.Y.)*,**111**(1978) pp. 61–151. - D. Cohen,
*An Introduction to Hilbert Space and Quantum Logic*, Springer-Verlag, 1989. This is a thorough and well-illustrated introduction. - Finkelstein, D. (1969),
*Matter, Space and Logic*, Boston Studies in the Philosophy of Science,**V**, p. 1969, doi:10.1007/978-94-010-3381-7_4, ISBN 978-94-010-3383-1. - A. Gleason. Measures on the Closed Subspaces of a Hilbert Space,
*Journal of Mathematics and Mechanics*, 1957. - R. Kadison. Isometries of Operator Algebras,
*Annals of Mathematics*, Vol. 54, pp. 325–38, 1951 - G. Ludwig.
*Foundations of Quantum Mechanics*, Springer-Verlag, 1983. - G. Mackey.
*Mathematical Foundations of Quantum Mechanics*, W. A. Benjamin, 1963 (paperback reprint by Dover 2004). - R. Omnès.
*Understanding Quantum Mechanics*, Princeton University Press, 1999. (Discusses logical and philosophical issues of quantum mechanics, with careful attention to the history of the subject). - N. Papanikolaou.
*Reasoning Formally About Quantum Systems: An Overview*, ACM SIGACT News, 36(3), pp. 51–66, 2005. - C. Piron.
*Foundations of Quantum Physics*, W. A. Benjamin, 1976. - Hermann Weyl.
*The Theory of Groups and Quantum Mechanics*, Dover Publications, 1950. - A. Whitaker.
*The New Quantum Age: From Bell's Theorem to Quantum Computation and Teleportation*, Oxford University Press, 2011, ISBN 978-0-19-958913-5 - Stephen Hawking.
*The Dreams that Stuff is Made of*, Running Press, 2011, ISBN 978-0-76-243434-3 - A. Douglas Stone.
*Einstein and the Quantum, the Quest of the Valiant Swabian*, Princeton University Press, 2006. - Richard P. Feynman.
*QED: The Strange Theory of Light and Matter*. Princeton University Press, 2006. Print.

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