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Diffstat (limited to 'gsl-1.9/doc/specfunc-coupling.texi')
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diff --git a/gsl-1.9/doc/specfunc-coupling.texi b/gsl-1.9/doc/specfunc-coupling.texi new file mode 100644 index 0000000..3efd9fe --- /dev/null +++ b/gsl-1.9/doc/specfunc-coupling.texi @@ -0,0 +1,109 @@ +@cindex coupling coefficients +@cindex 3-j symbols +@cindex 6-j symbols +@cindex 9-j symbols +@cindex Wigner coefficients +@cindex 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}. + +@menu +* 3-j Symbols:: +* 6-j Symbols:: +* 9-j Symbols:: +@end menu + +@node 3-j Symbols +@subsection 3-j Symbols + +@deftypefun double gsl_sf_coupling_3j (int @var{two_ja}, int @var{two_jb}, int @var{two_jc}, int @var{two_ma}, int @var{two_mb}, int @var{two_mc}) +@deftypefunx int gsl_sf_coupling_3j_e (int @var{two_ja}, int @var{two_jb}, int @var{two_jc}, int @var{two_ma}, int @var{two_mb}, int @var{two_mc}, gsl_sf_result * @var{result}) +These routines compute the Wigner 3-j coefficient, +@tex +\beforedisplay +$$ +\pmatrix{ja & jb & jc\cr + ma & mb & mc\cr} +$$ +\afterdisplay +@end tex +@ifinfo + +@example +(ja jb jc + ma mb mc) +@end example + +@end ifinfo +@noindent +where the arguments are given in half-integer units, @math{ja} = +@var{two_ja}/2, @math{ma} = @var{two_ma}/2, etc. +@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW +@end deftypefun + + +@node 6-j Symbols +@subsection 6-j Symbols + +@deftypefun double gsl_sf_coupling_6j (int @var{two_ja}, int @var{two_jb}, int @var{two_jc}, int @var{two_jd}, int @var{two_je}, int @var{two_jf}) +@deftypefunx int gsl_sf_coupling_6j_e (int @var{two_ja}, int @var{two_jb}, int @var{two_jc}, int @var{two_jd}, int @var{two_je}, int @var{two_jf}, gsl_sf_result * @var{result}) +These routines compute the Wigner 6-j coefficient, +@tex +\beforedisplay +$$ +\left\{\matrix{ja & jb & jc\cr + jd & je & jf\cr}\right\} +$$ +\afterdisplay +@end tex +@ifinfo + +@example +@{ja jb jc + jd je jf@} +@end example + +@end ifinfo +@noindent +where the arguments are given in half-integer units, @math{ja} = +@var{two_ja}/2, @math{ma} = @var{two_ma}/2, etc. +@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW +@end deftypefun + + +@node 9-j Symbols +@subsection 9-j Symbols + +@deftypefun double gsl_sf_coupling_9j (int @var{two_ja}, int @var{two_jb}, int @var{two_jc}, int @var{two_jd}, int @var{two_je}, int @var{two_jf}, int @var{two_jg}, int @var{two_jh}, int @var{two_ji}) +@deftypefunx int gsl_sf_coupling_9j_e (int @var{two_ja}, int @var{two_jb}, int @var{two_jc}, int @var{two_jd}, int @var{two_je}, int @var{two_jf}, int @var{two_jg}, int @var{two_jh}, int @var{two_ji}, gsl_sf_result * @var{result}) +These routines compute the Wigner 9-j coefficient, +@tex +\beforedisplay +$$ +\left\{\matrix{ja & jb & jc\cr + jd & je & jf\cr + jg & jh & ji\cr}\right\} +$$ +\afterdisplay +@end tex +@ifinfo + +@example +@{ja jb jc + jd je jf + jg jh ji@} +@end example + +@end ifinfo +@noindent +where the arguments are given in half-integer units, @math{ja} = +@var{two_ja}/2, @math{ma} = @var{two_ma}/2, etc. +@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW +@end deftypefun + |