| @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 |
| |
