Definitions

# Semiclassical

[sem-ee-klas-i-kuhl, sem-ahy-]
In physics, the adjective semiclassical has different precise meanings depending on the context. All these meanings usually refer to some approximation, limit or situation that combines quantum and classical aspects in a given problem. Some of the possible significations are the following:

First, semiclassical approximation may refer to quantum-mechanical calculations that are obtained by considering a small perturbation of a classical calculation, for example the WKB approximation in non-relativistic quantum mechanics or the loop expansion or the instanton methods in quantum field theory. In quantum field theory, a semiclassical correction arises from one-loop Feynman diagrams. The semiclassical effective action is

$Gamma\left[phi\right]=S\left[phi\right]+frac\left\{1\right\}\left\{2\right\}textrm\left\{Tr\right\}left\left[ln \left\{S^\left\{\left(2\right)\right\}\left[phi\right]\right\}right\right]+...$

Second, in the context of open quantum systems and measurement theory, where one considers the dynamics of a given quantum system in interaction with an environment, the semiclassical regime may refer to the situation in which the wavefunction of the system is approximately peaked around the solution of the corresponding classical equations of motion. Corrections to the classical trajectory and the dispersion of the solution around the mean value are usually considered.

Third, semiclassical gravity is the approximation to the yet unknown theory of quantum gravity in which one treats matter fields as being quantum and the gravitational field as being classical. The classical Einstein equations are computed with the expectation value of the quantum matter fields in the classical background. Semiclassical gravity has applications in black hole physics and physical cosmology.

A semiclassical approximation is any high frequency approximation (or "high energy approximation"), less extreme than classical mechanics, that is used to approximate quantum mechanics.

Fourthly, certain early theories in quantum mechanics, notably the Bohr model of the hydrogen atom, are sometimes called semi-classical, as they incorporate the newer quantum ideas into an essentially classical framework.

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