σ[1]=({{0, 1}, {1, 0}});σ[2]=({{0, -I}, {I, 0}});σ[3]=({{1, 0}, {0, -1}});

l[3]=({{1, 0, 0}, {0, 0, 0}, {0, 0, -1}});lp=({{0, (Sqrt[2]), 0}, {0, 0, (Sqrt[2])}, {0, 0, 0}});lm=({{0, 0, 0}, {(Sqrt[2]), 0, 0}, {0, (Sqrt[2]), 0}});

l[1]=(lp+lm)/2;l[2]=(((lp-lm))/(2I));

Sum[l[p].l[p],{p,3}]

op[a_,b_]:=KroneckerProduct[a,b]

h=Sum[op[σ[p],l[p]],{p,3}]

Eigenvalues[h]