UEC Education System

Wingner の 3j 記号 と クレプシュ・ゴルダン係数

# This maple procedure calculate Winger's symbol, 3J and CG coefficients
#
#                                     Created by R. Saito  6/6/92
#
# (6,90) definition of delta;
#
delta:=proc(j1,j2,j)
if abs(j1-j2) <= j and j <= (j1+j2) then
sqrt( (j1+j2-j)! * (j1+j-j2)! * (j2+j-j1)! / (j1+j2+j+1)! );
else 0; fi;
end;
#                    (6.92)
#      Wigner 3j's symbol  = | j1 j2 j3 |
#                            | m1 m2 m3 |
w3j:=proc(j1,j2,j3,m1,m2,m3)
local z,zmin,zmax;
if ((m1+m2+m3) <> 0 ) or (abs(m1) > j1)  or (abs(m2) > j2) or (abs(m3) > j3)
     or (abs(j1-j2) > j3) or (j3 > (j1+j2)) or (j1<0) or (j2<0) or (j3<0)
then 0;
else
zmin:=0; zmax:=j1+j2-j3;
if (j1-m1) < zmax then zmax:=(j1-m1); fi;
if (j2+m2) < zmax then zmax:=(j2+m2); fi;
if (j3-j2+m1) < 0 then zmin:=abs(j3-j2+m1); fi;
if (j3-j1-m2) < 0 and abs(j3-j1-m2) > zmin then zmin:=abs(j3-j1-m2); fi;
if zmin > zmax then 0; else
sum((-1)**(j1-j2-m3+z) /
   (z!*(j1+j2-j3-z)!*(j1-m1-z)!*(j2+m2-z)!*(j3-j2+m1+z)!*(j3-j1-m2+z)!),
    z=zmin..zmax)
 *delta(j1,j2,j3)*sqrt((j1+m1)!*(j1-m1)!*(j2+m2)!*(j2-m2)!*(j3+m3)!*(j3-m3)!);
fi;
fi;
end;
#                                                                  (6,91)
#  Clebsch-Gordan coefficient < j1, m1, j2, m2  | J, M >
# 
cg:=proc(j1,m1,j2,m2,j,m)
simplify((-1)**(j1-j2+m)*sqrt(2*j+1)*w3j(j1,j2,j,m1,m2,-m));
end;