Semiclassical physics
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In physics, semiclassical refers to a theory in which one part of a system 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.
History
[edit]Max Planck 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.[1][2] 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).[1][2]
Instances
[edit]Some examples of a semiclassical approximation include:
- WKB approximation: electrons in classical external electromagnetic fields.
- semiclassical gravity: quantum field theory within a classical curved gravitational background (see general relativity).
- 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, 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
[edit]- Bohr model
- Correspondence principle
- Classical limit
- Eikonal approximation
- Einstein–Brillouin–Keller method
- Old quantum theory
References
[edit]- ^ a b Liboff, Richard L. (1984-02-01). "The correspondence principle revisited". Physics Today. 37 (2): 50–55. doi:10.1063/1.2916084. ISSN 0031-9228.
- ^ a b Planck, Max (1906). Vorlesungen über die Theorie der Warmestrahlung. Leipzig: Verlag von Johann Ambrosius Barth.
- R. Resnick; R. Eisberg (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles (2nd ed.). John Wiley & Sons. ISBN 978-0-471-87373-0.
- P.A.M. Dirac (1981). Principles of Quantum Mechanics (4th ed.). Clarendon Press. ISBN 978-0-19-852011-5.
- W. Pauli (1980). General Principles of Quantum Mechanics. Springer. ISBN 3-540-09842-9.
- R.P. Feynman; R.B. Leighton; M. Sands (1965). Feynman Lectures on Physics. Vol. 3. Addison-Wesley. ISBN 0-201-02118-8.
- C.B. Parker (1994). McGraw-Hill Encyclopaedia of Physics (2nd ed.). McGraw-Hill. ISBN 0-07-051400-3.
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