# Quantum physics

The quantum physics includes all phenomena and effects that are based on certain variables but can not take on any value, only fixed, discrete values (see quantization ). This also includes the wave-particle dualism , the indeterminacy of physical processes and their inevitable influence through observation. Quantum physics includes all observations, theories , models and concepts to the quantum theory of Max Planck decline. Planck's hypothesis had become necessary around 1900 because classical physics e.g. B. had reached its limits in the description of light or the structure of matter .

The differences between quantum physics and classical physics are particularly evident in the microscopic (e.g. structure of atoms and molecules ) or in particularly "pure" systems (e.g. superconductivity and laser radiation ). But even everyday things such as the chemical or physical properties of various substances ( color , ferromagnetism , electrical conductivity , etc.) can only be understood in terms of quantum physics.

The theoretical quantum physics includes the quantum mechanics and quantum field theory . The former describes the behavior of quantum objects under the influence of fields . The latter also treats the fields as quantum objects. The predictions of both theories agree extremely well with the results of experiments.

An important open question is the relationship to general relativity . Despite great efforts towards a unified theory , it has not yet been possible to summarize these great physical theories of the 20th century in one theory of quantum gravity .

## Quantum Physics Theories

### Early quantum theories

Even before the development of quantum mechanics, there were discoveries that postulate the quantization of certain quantities and sometimes justify it with the wave-particle duality, but do not allow deeper insights into the underlying mechanisms. In particular, these theories did not make predictions beyond their respective subject matter. In English usage , these precursors of quantum mechanics are called old quantum theory .

In 1900 Max Planck developed a formula to describe the measured frequency distribution of the radiation emitted by a black body , Planck's law of radiation , based on the assumption that the black body consists of oscillators with discrete energy levels . Planck viewed this quantification of energy as a property of matter and not of light itself. Light was only affected insofar as light in his model could only exchange energy with matter in certain portions because only certain energy levels are possible in matter. He found the connection between the energy portion and the frequency of the light . ${\ displaystyle \ Delta E}$${\ displaystyle \ nu}$${\ displaystyle \ Delta E = h \ nu}$

Albert Einstein expanded these concepts and in 1905 proposed a quantization of the energy of light itself to explain the photoelectric effect . The photoelectric effect consists in the fact that light of certain colors can release electrons from metal surfaces . The light beam can only deliver the same amount of energy to each individual electron, which is also proportional to the frequency, i.e. a property of the light. From this, Einstein concluded that the energy levels are not only quantized within matter, but that light also only consists of certain energy portions, the light quanta . This concept is not compatible with a pure wave nature of light. So it had to be assumed that the light is neither a classical wave nor a classical particle flow, but behaves sometimes this way.

In 1913, Niels Bohr used the concept of quantized energy levels to explain the spectral lines of the hydrogen atom . The Bohr model of the atom named after him assumes that the electron in the hydrogen atom revolves around the nucleus with a certain energy . The electron is still regarded as a classical particle , with the only restriction that it can only have certain energies and, contrary to classical electrodynamics , when it circles the nucleus with such energy, it does not generate an electromagnetic wave, i.e. it does not emit any energy. The assumptions used by Bohr were experimentally confirmed in the Franck-Hertz experiment in 1914. Bohr's atomic model was expanded to include some concepts such as elliptical orbits of the electron, especially by Arnold Sommerfeld , in order to also be able to explain the spectra of other atoms. However, this objective has not been achieved satisfactorily. In addition, Bohr could not give any justification for his postulates except that the hydrogen spectrum could be explained with it; his model did not lead to deeper insight.

In 1924 Louis de Broglie published his theory of matter waves , according to which any matter can have a wave character and, conversely, waves can also have a particle character. With the help of his theory, the photoelectric effect and Bohr's atomic model could be traced back to a common origin. The orbits of the electron around the atomic nucleus were understood as standing waves of matter . The calculated wavelength of the electron and the lengths of the orbits according to Bohr's model agreed well with this concept. An explanation of the other atomic spectra was still not possible.

De Broglie's theory was confirmed three years later in two independent experiments that demonstrated the diffraction of electrons. The British physicist George Paget Thomson led a electron beam through a thin metal film and observed the predicted by de Broglie interference pattern . As early as 1921, a similar experiment by Clinton Davisson and Charles Kunsman at Bell Labs showed diffraction patterns in an electron beam reflected by nickel , but these were not yet interpreted as interference. Davisson and his assistant Lester Germer repeated the experiment in 1927 and explained the clear diffraction patterns observed using de Broglie's wave theory.

### Quantum mechanics

Modern quantum mechanics began in 1925 with the formulation of matrix mechanics by Werner Heisenberg , Max Born and Pascual Jordan . A few months later Erwin Schrödinger developed wave mechanics and the Schrödinger equation using a completely different approach - based on De Broglie's theory of matter waves . Shortly afterwards, Schrödinger was able to prove that his approach is equivalent to matrix mechanics.

The new approaches by Schrödinger and Heisenberg contain a new view of observable physical quantities, so-called observables . These had previously been viewed as quantities that have certain numerical values ​​in every state of a system, such as (for a particle in one dimension ) the respective location or momentum . In contrast, Heisenberg and Schrödinger tried to expand the term observable in such a way that it would be compatible with the diffraction at the double slit . If an additional measurement determines which of the slits it flies through for each particle , no double slit interference pattern is obtained, but two individual slit patterns. At the end of this measurement the state of the observed particle is different from before. Observables are therefore formally understood as functions that convert one state into another. Furthermore, each particle has to "somehow" fly through both gaps so that an interference pattern can be explained at all. Both possibilities have to be ascribed to the state of each individual (!) Particle during the flight, whereby exactly one is realized during observation. As a result, the state of a particle can no longer be determined by unambiguous values ​​such as position and momentum, but has to be separated from the observables and their values. During a measurement process, the state is converted into one of the so-called eigenstates of the observables, which is now assigned a unique real measurement value . This concept of the quantum mechanical state is therefore not compatible with the concept of the (mathematically precise) trajectory in the older quantum theory. Mathematically, a quantum mechanical state is represented by a wave function or (less clearly) by a state vector .

A consequence of this new concept of observables is that it is formally not possible to let any two observables act on a state without specifying a sequence. If the sequence of two measurement processes is not important (e.g. measurement of the x and y coordinates), they are called interchangeable. Otherwise (e.g. measurement of x-coordinate and x-pulse) their sequence must be determined, and in precisely these cases the second measurement changes the state generated by the first measurement one more time. Therefore, a subsequent repetition of the first measurement would also have a different result. It is therefore possible that two observables, if they act on a state in a different order, can produce different final states. If the order of the measurement is decisive for two observables because the final states are otherwise different, this leads to a so-called uncertainty relation . This was first described by Heisenberg in 1927 for place and impulse. These relations attempt to quantitatively describe the scatter of the measured values ​​when the observables are interchanged, and thus the difference in the final states.

In 1927 Bohr and Heisenberg formulated the Copenhagen interpretation , which is also known as the orthodox interpretation of quantum mechanics. It was based on Max Born's suggestion that the square of the absolute value of the wave function, which describes the state of a system, should be understood as the probability density . The Copenhagen Interpretation is still the interpretation of quantum mechanics advocated by most physicists, although there are now numerous other interpretations.

In the years from 1927 onwards, Paul Dirac combined quantum mechanics with the special theory of relativity . He also first introduced the use of operator theory including the Bra-Ket notation and described this mathematical calculation in a monograph in 1930 . At the same time, John von Neumann formulated the strict mathematical basis for quantum mechanics, such as B. the theory of linear operators on Hilbert spaces , which he described in a monograph in 1932.

The use of the term quantum physics was first documented in 1929 in Max Planck's lecture The World View of New Physics . The results formulated in this development phase are still valid today and are generally used to describe quantum mechanical tasks.

### Quantum field theory

From 1927, attempts were made to apply quantum mechanics not only to particles but also to fields , from which the quantum field theories arose. The first results in this area were achieved by Paul Dirac, Wolfgang Pauli , Victor Weisskopf and Pascual Jordan . In order to be able to describe waves, particles and fields uniformly, they are understood as quantum fields, similar objects to observables. However, they do not have to meet the property of real valency . This means that the quantum fields do not necessarily represent measurable quantities. However, the problem arose that the calculation of complicated scattering processes of quantum fields gave infinite results. Calculating the simple processes alone, however, often produces results that deviate significantly from the measured values.

It was not until the late 1940s that the problem of infinity could be circumvented with renormalization . This made the formulation of quantum electrodynamics possible by Richard Feynman , Freeman Dyson , Julian Schwinger and Shin'ichirō Tomonaga . Quantum electrodynamics describes electrons , positrons and the electromagnetic field in a consistent way for the first time, and the measurement results it predicted could be confirmed very precisely. The concepts and methods developed here were used as models for further quantum field theories developed later.

The theory of quantum chromodynamics was worked out in the early 1960s. The form of the theory known today was formulated in 1975 by David Politzer , David Gross and Frank Wilczek . Building on the pioneering work of Julian Seymour Schwinger , Peter Higgs , Jeffrey Goldstone and Sheldon Glashow , Steven Weinberg and Abdus Salam were able to independently show how the weak nuclear force and quantum electrodynamics can be merged into the theory of the electroweak interaction .

To this day, quantum field theory is an active research area that has developed many new methods. It is the basis of all attempts to formulate a unified theory of all basic forces . In particular, supersymmetry , string theory , loop quantum gravity and twistor theory are largely based on the methods and concepts of quantum field theory.

## Overview of the research history

The following list does not claim to be complete.

discovery Explorer Discovery year Remarks
Line spectra , spectrometry Bunsen , Kirchhoff 1860
Photo effect Reverb wax 1886
Rydberg formula Rydberg 1888 Empirical formula for the hydrogen spectrum, which could only be theoretically substantiated by Bohr's atomic model.
Field emission of electrons Wood 1897 First observation of the tunnel effect , which was understood much later, however.
Planck's law of radiation Planck 1900 First application of the quantum hypothesis; "Birth hour" of quantum physics.
Photons Einstein 1905 Radiation is quantized.
Superconductivity Kamerlingh Onnes 1911
Franck-Hertz experiment Franck , Hertz 1911-1914 There are discrete energy levels in atoms.
Bohr's atomic model Bohr 1913 First quantum physical atomic model; Refined by Sommerfeld in 1916 ( Bohr-Sommerfeld's atomic model ), but now obsolete.
Compton effect Compton 1922 Photons have an impulse.
Stern-Gerlach experiment Stern , Gerlach 1922 The angular momentum is quantized.
Matter waves de Broglie 1924 Justification of the wave-particle dualism
Die mechanics Heisenberg 1925 First strict formulation of quantum mechanics
Spin of electrons Goudsmit , Uhlenbeck , Pauli 1925
Wave mechanics Schrodinger 1926 Mathematically equivalent to matrix mechanics
Probability interpretation Born 1926 Wave function as probability amplitude
Solution to the hydrogen problem Schrodinger 1926 Energy levels and orbitals of the electrons in the hydrogen atom
Fermi-Dirac statistics Fermi , Dirac 1926 Theory of the fermion gas and thus the basis for solid-state physics , especially for semiconductors .
Uncertainty relation Heisenberg 1927 Place and impulse are not at the same time precisely determined.
Davisson-Germer experiment Davisson , Germer 1927 Experimental confirmation of the matter waves postulated by de Broglie.
Relativistic quantum mechanics Klein , Gordon , Dirac 1926-1928
Tunnel effect Gamow , Hund et al 1926-1928 Theoretical explanation for the alpha decay and the field emission
Nuclear magnetic resonance Rabi 1936
Superfluidity Kapiza et al 1938
transistor Shockley , Brattain , Bardeen 1945 Microelectronics was “born”
Quantum electrodynamics Feynman , Tomonaga , Schwinger 1947
Semiconductor solar cell Pearson , Fuller , Chapin 1954 Bell Laboratories
neutrino Cowan , pure 1956 Predicted by Pauli in 1930.
BCS theory Bardeen , Cooper , Schrieffer 1957 Quantum physics justification of superconductivity
laser Maiman 1960
Quarks Gell man 1961
Bell's inequality Bell 1964 There are no local hidden parameters that determine the behavior of a quantum physical system.
Electroweak interaction Glass show , salam , vineyard 1967 Union of electromagnetic and weak interaction
CCD sensor Boyle , Smith 1969 Basic building block for the digital camera
microprocessor Shima , Hoff , Mazor , Faggin 1970-1971 Texas Instruments , Intel
Quantum chromodynamics Gell-Mann et al 1972 Theory of the strong interaction , an integral part of the standard model
Magnetic resonance imaging Mansfield , Lauterbur 1973 Use of nuclear magnetic resonance for an imaging procedure in medicine
Scanning tunnel microscope Binnig , Rohrer 1981
Quantum Hall Effect from Klitzing 1985
Flash memory Harari 1994 SanDisk

Application of the tunnel effect in storage media

Bose-Einstein condensate Cornell , Ketterle , Wieman 1995 Fourth state of matter predicted by Albert Einstein in 1924
Quantum teleportation Zeilinger 1997 In 1935 Einstein, Podolski and Rosen considered this quantum entanglement effect to be paradoxical .
 Legend: Experimental physics Theoretical physics Technical application

## literature

Wiktionary: quantum physics  - explanations of meanings, word origins, synonyms, translations
Commons : Quantum Physics  - collection of images, videos and audio files

## Individual evidence

1. M. Planck: On the theory of the law of energy distribution in the normal spectrum , negotiations of the German physical society 2 (1900) No. 17, pp. 237–245, Berlin (presented on December 14, 1900).
2. A. Einstein: About a heuristic point of view relating to the generation and transformation of light , Annalen der Physik 17 (1905), pp. 132-148. ( PDF ).
3. ^ L. de Broglie: Recherches sur la théorie des Quanta , doctoral thesis. English translation (translated by AF Kracklauer): Ann. de Phys., 10e series, t. III, (1925).
4. ^ GP Thomson: The Diffraction of Cathode Rays by Thin Films of Platinum. Nature 120 (1927), 802.
5. C. Davisson, CH Kunsman: THE SCATTERING OF ELECTRONS BY NICKEL In: Science Vol. 54 p. 1104
6. C. Davisson and LH Germer: Diffraction of Electrons by a Crystal of Nickel In: Phys. Rev. 30, No. 6, 1927, doi : 10.1103 / PhysRev.30.705 .
7. ^ W. Heisenberg: About quantum theoretical reinterpretation of kinematic and mechanical relationships Zeitschrift für Physik 33 (1925), pp. 879-893.
8. M. Born, P. Jordan: Zur Quantenmechanik , Zeitschrift für Physik 34 (1925), 858
9. ^ M. Born, W. Heisenberg, P. Jordan: Zur Quantenmechanik II , Zeitschrift für Physik 35 (1926), 557.
10. E. Schrödinger: Quantization as an eigenvalue problem I , Annalen der Physik 79 (1926), 361–376. E. Schrödinger: Quantization as an eigenvalue problem II , Annalen der Physik 79 (1926), 489-527. E. Schrödinger: Quantization as an eigenvalue problem III , Annalen der Physik 80 (1926), 734–756. E. Schrödinger: Quantization as an eigenvalue problem IV , Annalen der Physik 81 (1926), 109-139.
11. ^ E. Schrödinger: On the relationship between Heisenberg-Born-Jordan quantum mechanics and mine , Annalen der Physik 79 (1926), 734-756.
12. ^ PAM Dirac: "Principles of Quantum Mechanics" , Oxford University Press, 1958, 4th. ed., ISBN 0-19-851208-2 .
13. John von Neumann: "Mathematical Foundations of Quantum Mechanics" , Springer Berlin, 1996, 2nd edition. Engl. (Authorized) edition (translated by R. T Beyer): “Mathematical Foundations of Quantum Mechanics” , Princeton Univ. Press, 1955 (there p. 28 sqq.)
14. M. Planck, Das Weltbild der neue Physik , monthly books for mathematics, Springer, Vienna, Vol. 36 (1929), pp. 387-410. Extract from google books .
15. ^ Richard Feynman: QED. The Strange Theory of Light and Matter 1987, ISBN 3-492-21562-9  - An Easy To Understand Introduction to Quantum Electrodynamics.
16. For sources and further information, please refer to the linked main articles.
17. Friedrich Hund, the tunnel effect and the shining stars on Deutschlandfunk broadcast on February 4, 2016.