What is quantum physics

The Quantum physics is the area of ​​physics that deals with the behavior and interaction of the smallest particles.

On the scale of molecules and below, experimental measurements provide results that contradict classical mechanics. In particular, certain quantities are quantized, that is, they only appear in certain portions - the so-called "quanta". In addition, no meaningful distinction between particles and waves is possible, since the same object behaves either as a wave or as a particle, depending on the type of investigation. This is called wave-particle dualism. The theories of quantum physics seek explanations for these phenomena in order to, among other things. enable the prediction of measurement results on small length and mass scales.

Quantum Physics Theories

Semiclassical quantum theories

Main article: Semiclassical quantum theory

Semiclassical, old or early quantum theories are theories 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 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[1]. Planck viewed this quantification of energy as a property of matter and not of light itself. Light was only affected to the extent that light in his model could only exchange energy with matter in certain portions, because only certain energy levels are possible in matter .

Albert Einstein expanded this concept and in 1905 proposed a quantization of the energy of light itself in order to explain the photoelectric effect[2]. The photoelectric effect describes the observation that the amounts of energy that a light beam can give off to matter are 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 portions of energy. This concept is incompatible with a pure wave nature of light. So it had to be assumed that the light behaves neither like a classical wave nor like a classical particle flow.

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 circles the nucleus at a certain energy level. The electron is still regarded as a classical particle, with the only restriction that it can only have certain energies. The Bohr model of the atom was extended by some concepts such as elliptical orbits of the electron, especially by Arnold Sommerfeld, in order to be able to explain the spectra of other atoms. However, this objective has not been achieved satisfactorily. In addition, Bohr gave no justification for his postulates, so that his model did not offer any deeper insights.

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[3]. 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. British physicist George Paget Thomson directed an electron beam through a thin metal film and observed the interference patterns predicted by de Broglie[4]. In a similar experiment carried out at Bell Labs as early as 1919, Clinton Davisson and his assistant Lester Germer observed the diffraction patterns of an electron beam reflected on a nickel crystal. However, they did not manage to explain it until 1927 with the help of De Broglie's wave theory.[5]

Quantum mechanics

Main article: Quantum mechanics

Modern quantum mechanics began in 1925 with the formulation of matrix mechanics by Werner Heisenberg, Max Born and Pascual Jordan[6][7][8]. A few months later Erwin Schrödinger invented wave mechanics and the Schrödinger equation using a completely different approach - based on De Broglie's theory of matter waves[9]. Shortly afterwards, Schrödinger was able to prove that his approach is equivalent to matrix mechanics. [10]

The new approaches by Schrödinger and Heisenberg included a new view of observable physical quantities, so-called Observables. These had previously been viewed as functions that assigned a number to a certain state of a system, namely the magnitude, such as position or momentum. On the other hand, Heisenberg and Schrödinger tried to expand the term observable in such a way that it would be compatible with diffraction at the double slit. If it is determined by measurement through which of the slits a particle is flying, then no double slit interference pattern is obtained, but two individual slit patterns. The measurement thus influences the state of the system. Observables are therefore understood as functions that map one state to another. As a result, the state of a system can no longer be determined by size values ​​such as position and momentum, but the state has to be separated from the observables and size values, so the concept of the trajectory has been replaced by the abstract concept of the quantum mechanical state. In a measurement process, the state is mapped to a so-called eigenstate of the observables, to which a real measured value is assigned. This is an additional "real valence condition" that observables must meet.

One consequence of this new concept of observables is that the sequence of several measurement processes has to be determined, since it is not possible to let two observables act on a state without specifying a sequence. The sequence of the measurement processes can be important for the result, so it is possible that two observables, if they act on a state in a different sequence, deliver 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. Heisenberg first described the location and impulse in 1927. These relations attempt to quantitatively describe the difference in the final states when the observables are swapped.

In 1927 Bohr and Heisenberg formulated the Copenhagen interpretation, which is also known as the orthodox interpretation of quantum mechanics. It was based on Born's suggestion to interpret the square of the absolute value of the wave function, which describes the state of a system, 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 of quantum mechanics.

In the years from around 1927 onwards, Paul Dirac combined quantum mechanics with the special theory of relativity. He also introduced the use of operator theory including the Bra-Ket notation for the first time and described this mathematical calculus in an important non-fiction book in 1930[11]. 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 1932 in his equally important non-fiction book[12]. The term "quantum physics" was first used in 1931 in Max Planck's book "The Universe in the Light of Modern Physics"[13]. The results formulated in this development phase are still valid today and are generally used to describe quantum mechanical tasks.

Quantum field theory

Main article: 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, objects similar to observables. However, they do not have to meet the property of "real value". 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 provides results that deviate significantly from the measured values.

It was only at the end of the 1940s that the problem of infinity could be circumvented with renormalization. This enabled the formulation of quantum electrodynamics by Richard Feynman, Freeman Dyson, Julian Schwinger, and Sin-Itiro 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 that were 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.


  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 concerning the generation and transformation of light“, Annalen der Physik 17 (1905), pp. 132-148. [1]
  3. L. de Broglie: "Research on theory of Quanta", PhD thesis. English translation (translated by A.F. Kracklauer): Ann. de Phys., 10e series, t. III, (1925)
  4. G. P. Thomson: "The Diffraction of Cathode Rays by Thin Films of Platinum."Nature 120 (1927), 802
  5. C. Davisson and L. H. Germer: Diffraction of Electrons by a Crystal of Nickel In: Phys. Rev.. 30, No. 6, 1927 doi: 10.1103 / PhysRev.30.705
  6. W. Heisenberg: "About quantum theoretical reinterpretation of kinematic and mechanical relationships“Zeitschrift für Physik 33 (1925), pp. 879-893.
  7. M. Born, P. Jordan: "To quantum mechanics", Zeitschrift für Physik 34 (1925), 858
  8. M. Born, W. Heisenberg, P. Jordan: "On quantum mechanics II", Zeitschrift für Physik 35 (1926), 557
  9. 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
  10. E. Schrödinger: "About the relationship between Heisenberg-Born-Jordan quantum mechanics and mine“, Annalen der Physik 79 (1926), 734-756.
  11. P. A. M. Dirac: "Principles of Quantum Mechanics", Oxford University Press, 1958, 4th. ed, ISBN 0-198-51208-2
  12. John von Neumann: "Mathematical Foundations of Quantum Mechanics", Springer Berlin, 1996, 2nd edition. English (authorized) edition (translated by R. T Beyer): "Mathematical Foundations of Quantum Mechanics", Princeton Univ. Press, 1955 (there p. 28 sqq.)
  13. M. Planck: "The Universe in the Light of Modern Physics", WW Norton & Company, Inc., New York, 1931

Category: quantum physics