\hat{H}=\frac{1}{2m}\hat{p}^2=\frac{1}{2m}\left(\hat{p_x}^2+\hat{p_y}^2+\hat{p_z}^2\right)=\hat{H}_1^{1D}+\hat{H}_2^{1D}+\hat{H}_3^{1D}