In
physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
, semiclassical refers to a theory in which one part of a
system
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its open system (systems theory), environment, is described by its boundaries, str ...
is described
quantum mechanically, whereas the other is treated
classically. For example, external
fields will be constant, or when changing will be classically described. In general, it incorporates a development in
powers of the
Planck constant, resulting in the classical physics of power 0, and the first nontrivial approximation to the power of (−1). In this case, there is a clear link between the quantum-mechanical system and the associated semi-classical and classical approximations, as it is similar in appearance to the transition from
physical optics to
geometric optics
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician ...
.
History
Max Planck
Max Karl Ernst Ludwig Planck (; ; 23 April 1858 – 4 October 1947) was a German Theoretical physics, theoretical physicist whose discovery of energy quantum, quanta won him the Nobel Prize in Physics in 1918.
Planck made many substantial con ...
was the first to introduce the idea of quanta of energy in 1900 while studying
black-body radiation. In 1906, he was also the first to write that quantum theory should replicate classical mechanics at some limit, particularly if the
Planck constant ''h'' were infinitesimal.
With this idea he showed that
Planck's law for thermal radiation leads to the
Rayleigh–Jeans law, the classical prediction (valid for large
wavelength).
Instances
Some examples of a semiclassical approximation include:
*
WKB approximation: electrons in classical external
electromagnetic fields.
*
semiclassical gravity
Semiclassical gravity is an approximation to the theory of quantum gravity in which one treats matter and energy fields as being quantum and the gravitational field as being classical.
In semiclassical gravity, matter is represented by quantum ...
:
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
within a classical
curved gravitational background (see
general relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
).
*
quantum chaos: quantization of classical
chaotic systems.
* magnetic properties of materials and astrophysical bodies under the effect of large magnetic fields (see for example
De Haas–Van Alphen effect)
*
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
: only
Feynman diagrams with at most a single closed loop (see for example
one-loop Feynman diagram) are considered, which corresponds to the powers of the Planck constant.
See also
*
Bohr model
In atomic physics, the Bohr model or Rutherford–Bohr model was a model of the atom that incorporated some early quantum concepts. Developed from 1911 to 1918 by Niels Bohr and building on Ernest Rutherford's nuclear Rutherford model, model, i ...
*
Correspondence principle
*
Classical limit
*
Eikonal approximation
*
Einstein–Brillouin–Keller method
*
Old quantum theory
References
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*
Quantum mechanics
Quantum field theory
Quantum chemistry
Theoretical chemistry
Computational chemistry
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