Semiclassical physics

Semiclassical physics, or simply 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 Planck's 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.

Instances

Three 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

In quantum field theory, in the semiclassical approximation only Feynman diagrams with at most a single closed loop (see for example one-loop Feynman diagram) are considered, this corresponds to the powers of Planck's constant. In chaos theory, the observation semiclassical approximations is a topic of current research.

See also

• Eikonal approximation
• Correspondence principle
• Bohr model
• 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 9-780198-520115.
• W. Pauli (1980). General Principles of Quantum Mechanics. Springer. ISBN 3-54009-8429.
• R.P. Feynman, R.B. Leighton, M. Sands (1965). Feynman Lectures on Physics 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.