diff --git a/ho_basis.jl b/ho_basis.jl
index e1cc7ed..d97f53a 100644
--- a/ho_basis.jl
+++ b/ho_basis.jl
@@ -49,7 +49,23 @@ end
 
 get_V_matrix(V_l, ls, ns) = throw("unimplemented")
 
-get_T_matrix(ns, ls) = throw("unimplemented")
+function sp_T_matrix(ns, ls)
+    mat = zeros(length(ns), length(ns))
+    for idx in CartesianIndices(mat)
+        (i, j) = Tuple(idx)
+        if ls[i] == ls[j]
+            mat[idx] = ls[i]
+            if ns[i] == ns[j]
+                mat[idx] += 1/4 * (4*ns[j] + 3)
+            elseif ns[i] == ns[j] + 1
+                mat[idx] += -1/4 * sqrt((2*ns[j] + 2) * (2*ns[j] + 3))
+            elseif ns[i] == ns[j] - 1
+                mat[idx] += -1/4 * sqrt((2*ns[j] + 1) * 2*ns[j])
+            end
+        end
+    end
+    return mat
+end
 
 get_H_matrix(V_l, ns, ls) = get_T_matrix(ns, ls) + get_V_matrix(V_l, ns, ls)