Semiclassical physics
Use of both classical and quantum physics to analyze a system
From Wikipedia, the free encyclopedia
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 Planck's 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 Planck's constant 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.
