In this paper, we study the 9B and 9Be mirror nuclei with shell and cluster models. The modified Eckart plus Coulomb repulsive potentials are selected to describe the interaction between particles. By solving the Schrödinger equation, the exact solution of this equation is obtained by the parametric Nikiforov–Uvarov (PNU) method. The eigenvalues and wave function are calculated for 9B and 9Be. Our results are compared with experimental results, as well as results from other papers, and are in good agreement.