Summary: Let \(L=-\Delta_{H^n}+V\) be a Schrödinger operator on the Heisenberg group \(H^n\), where \(\Delta_{H^n}\)is the sublaplacian and the nonnegative potential \(V\) belongs to the reverse Hölder class \(B_{Q/2}\), where \(Q\) is the homogeneous dimension of \(H^n\). Let \(T_1=(-\Delta_{H^n}+V)^{-1}V\), \(T_2=(-\Delta_{H^n}+V)^{1/2}V^{1/2}\), and \(T_3=(-\Delta_{H^n}+V)^{-1/2}\nabla_{H^n}\). We verify that \([b, T_i]\), \(i = 1, 2, 3\), are bounded on some \(L^p(H^n)\), where \(b\in \text{BMO}(H^n)\). Note that the kernel of \(T_i\), \(i=1, 2, 3\), has no smoothness.