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.

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]

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.

• Bohr model
• Correspondence principle
• Classical limit
• Eikonal approximation
• Einstein–Brillouin–Keller method
• Old quantum theory

• 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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