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.. index::
single: coupling coefficients
single: 3-j symbols
single: 6-j symbols
single: 9-j symbols
single: Wigner coefficients
single: Racah coefficients
The Wigner 3-j, 6-j and 9-j symbols give the coupling coefficients for
combined angular momentum vectors. Since the arguments of the standard
coupling coefficient functions are integer or half-integer, the
arguments of the following functions are, by convention, integers equal
to twice the actual spin value. For information on the 3-j coefficients
see Abramowitz & Stegun, Section 27.9. The functions described in this
section are declared in the header file :file:`gsl_sf_coupling.h`.
3-j Symbols
-----------
.. function:: double gsl_sf_coupling_3j (int two_ja, int two_jb, int two_jc, int two_ma, int two_mb, int two_mc)
int gsl_sf_coupling_3j_e (int two_ja, int two_jb, int two_jc, int two_ma, int two_mb, int two_mc, gsl_sf_result * result)
These routines compute the Wigner 3-j coefficient,
.. only:: not texinfo
.. math::
\left(
\begin{array}{ccc}
ja & jb & jc \\
ma & mb & mc
\end{array}
\right)
.. only:: texinfo
| ( ja jb jc )
| ( ma mb mc )
where the arguments are given in half-integer units, :math:`ja` =
:data:`two_ja`/2, :math:`ma` = :data:`two_ma`/2, etc.
.. Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW
6-j Symbols
-----------
.. function:: double gsl_sf_coupling_6j (int two_ja, int two_jb, int two_jc, int two_jd, int two_je, int two_jf)
int gsl_sf_coupling_6j_e (int two_ja, int two_jb, int two_jc, int two_jd, int two_je, int two_jf, gsl_sf_result * result)
These routines compute the Wigner 6-j coefficient,
.. only:: not texinfo
.. math::
\left\{
\begin{array}{ccc}
ja & jb & jc \\
jd & je & jf
\end{array}
\right\}
.. only:: texinfo
| { ja jb jc }
| { jd je jf }
where the arguments are given in half-integer units, :math:`ja` =
:data:`two_ja`/2, :math:`ma` = :data:`two_ma`/2, etc.
.. Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW
9-j Symbols
-----------
.. function:: double gsl_sf_coupling_9j (int two_ja, int two_jb, int two_jc, int two_jd, int two_je, int two_jf, int two_jg, int two_jh, int two_ji)
int gsl_sf_coupling_9j_e (int two_ja, int two_jb, int two_jc, int two_jd, int two_je, int two_jf, int two_jg, int two_jh, int two_ji, gsl_sf_result * result)
These routines compute the Wigner 9-j coefficient,
.. only:: not texinfo
.. math::
\left\{
\begin{array}{ccc}
ja & jb & jc \\
jd & je & jf \\
jg & jh & ji
\end{array}
\right\}
.. only:: texinfo
| { ja jb jc }
| { jd je jf }
| { jg jh ji }
where the arguments are given in half-integer units, :math:`ja` =
:data:`two_ja`/2, :math:`ma` = :data:`two_ma`/2, etc.
.. Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW
|
