# User Contributed Dictionary

### Adjective

- Describing classical music of broad, popular appeal
- Describing any of various approximations to either relativistic or quantum mechanical physics that retains elements of classical physics

# Extensive Definition

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[\phi]=S[\phi]+\frac\textrm\left[\ln \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.

semiclassical in German: Semiklassische
Näherung

semiclassical in Estonian: Poolklassikalised
kvantteooriad

semiclassical in French: Régime
semi-classique