We present the analytical expressions of eigenstates and eigenenergies by using a parameter λ without the assumption of Bethe anzatz for three kinds of seven-bosonic-mode mixing models. The parameter is shown to be determined by the roots of a simple polynomial. We also demonstrate the exact analytical expressions of eigenstates and energies without any unknown parameter.
ZHAN Zhiming1,LI Weibin2,YOU Jun2,XIE Xiaotao2 & YANG Wenxing2 1.State Key Laboratory of Laser Technology,Huazhong University of Science and Technology,Wuhan 430074,China
