The Faddeev equations, named after their inventor
Ludvig Faddeev, are
equations that describe, at once, all the possible exchanges/
interactions in a system of three
particles in a fully
quantum mechanical formulation. They can be
solved iteratively.
In general, Faddeev equations need as input a
potential that describes the interaction between two individual particles. It is also possible to introduce a term in the equation in order to take also
three-body forces into account.
The Faddeev equations are the most often used non-
perturbative
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for wh ...
formulations of the quantum-mechanical three-body problem.
Unlike the three body problem in
classical mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...
, the quantum three body problem is
uniformly
Uniform distribution may refer to:
* Continuous uniform distribution
* Discrete uniform distribution
* Uniform distribution (ecology)
* Equidistributed sequence In mathematics, a sequence (''s''1, ''s''2, ''s''3, ...) of real numbers is said to be ...
soluble.
In
nuclear physics
Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter.
Nuclear physics should not be confused with atomic physics, which studies the ...
, the off the
energy shell nucleon-nucleon interaction has been studied by analyzing (n,2n) and (p,2p) reactions on
deuterium
Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two Stable isotope ratio, stable isotopes of hydrogen (the other being Hydrogen atom, protium, or hydrogen-1). The atomic nucleus, nucleus of a deuterium ato ...
targets, using the Faddeev Equations. The nucleon-nucleon interaction is expanded (approximated) as a
series of separable potentials. The
Coulomb interaction between two protons is a special problem, in that its expansion in separable potentials does not converge, but this is handled by matching the Faddeev solutions to long range Coulomb solutions, instead of to
plane waves.
Separable potentials are interactions that do not preserve a particle's location. Ordinary local
potentials can be expressed as sums of separable potentials. The physical nucleon-nucleon interaction, which involves exchange of
meson
In particle physics, a meson ( or ) is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticle ...
s, is not expected to be either local or separable.
References
* L.D. Faddeev, S.P. Merkuriev, Quantum Scattering Theory for Several Particle Systems, Springer, August 31, 1993, .
{{DEFAULTSORT:Faddeev Equations
Quantum mechanics
Nuclear physics
Equations