Semiclassical physics

In physics, the semiclassical approximation divides a system into two parts, one to be described quantum-mechanically, and the other to be treated classically. In general, it incorporates a series expansion in powers of the Planck constant, resulting in classical physics in the power of 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 semiclassical and classical approximations, as it is similar in appearance to the transition from physical optics to geometric optics.

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 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.
• Expansion around classical solution: Classical limit of quantum mechanics by continuous measurement.
• 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.