Generating the coupled spin basis

The basis vectors of the coupled spin (energy eigenstate) basis are generated using genVecs[].

genVecs[ {rep_,order_,scale_} ] := 
         Block[ { a={},n,j,m,q,newrep },
                n=Length[rep]-order;
                q=2(order+1);
                If[ order<(n-1) ,
                    For[ j=Abs[rep[[q]]-rep[[q-1]]],
                         j<=(rep[[q]]+rep[[q-1]]),
                         j++,
                         newrep=Insert[rep,j,q+1] ;
                         a=Join[a,
                           genVecs[{newrep,order+1,scale}]] ;
                       ] ;
                  ] ;
                If[ order==(n-1) ,
                    For[ m=-rep[[q-1]], m<=rep[[q-1]], m++,
                         a=Join[a,{{Join[rep,{m}],n-1,scale}}]
                       ] ;
                  ] ;
                Return[a] ;
              ]

The arguments of genVecs are rep, a list of the spin values, order, the order of the representation given, usually 0, and scale, the value of the amplitude to be assigned to the vectors generated. For example,
 
produces the list of four vectors with their order and scale.

Here the order has become 1 because one coupling has occurred between the two spins given.