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Racah

Racah is a surname of European origin that appears in the titles of several concepts in mathematics and physics. The name is most closely associated with the study of angular momentum in quantum mechanics and the algebraic framework used to handle recoupling of angular momenta.

In quantum mechanics and related fields, Racah coefficients, commonly referred to as Racah 6-j symbols or Wigner–Racah

The Racah algebra is an overarching term for the algebraic structure that governs the relations among angular-momentum

Racah polynomials are a family of orthogonal polynomials that emerge in the study of Racah coefficients and

Beyond these scientific uses, Racah also serves as a surname for individuals in science and other fields.

symbols,
arise
when
recoupling
three
angular
momenta.
They
provide
a
compact
way
to
transform
between
different
coupling
schemes
and
are
widely
used
in
atomic,
nuclear,
and
particle
physics
to
simplify
the
evaluation
of
matrix
elements.
operators
and
their
coupling
coefficients
in
the
Wigner–Eckart
framework.
This
algebra
underpins
the
consistency
relations
between
different
recoupling
coefficients
and
appears
in
various
representations
and
symmetry
analyses.
more
broadly
in
the
representation
theory
of
certain
Lie
algebras
and
quantum
groups.
They
form
part
of
the
discrete
end
of
the
Askey
scheme
of
hypergeometric
orthogonal
polynomials
and
connect
to
problems
in
combinatorics
and
mathematical
physics.
The
term
carries
a
legacy
in
the
language
of
angular-momentum
theory
and
its
mathematical
tools.