\hat{H}|\psi\rangle = \left(\hat{H}_1^{1D}+\hat{H}_2^{1D}+\hat{H}_1^{1D}\right)|\psi_1\rangle \otimes |\psi_2\rangle \otimes |\psi_3\rangle=\left[\left(\hat{H_1^{1D}|\psi_1\rangle\right)\otimes|\psi_2\rangle\otimes|\psi_3\rangle+|\psi_1\rangle\otimes\left(H_2^{1D}|\psi_2\rangle\right)\otimes|\psi_3\rangle+|\psi_1\rangle\otimes|\psi_2\rangle\otimes\left(H_3^{1D}|\psi_3\rangle\right]