History

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 Planck's constant ${\displaystyle h}$ 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

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

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

References

• 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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