Abstarct: The past decade to date, oxygen isotopes have been widely studied theoretically and empirically. Among the different oxygen isotopes, we select oxygen-16 isotope the which its core is even-even and Double magic. Since this isotope has 16 nucleons; the first forces between nucleons are discussed in many-body systems. Then we propose the shell model, shell model and collective model and cluster model and Considering these three models, we discuss to solve the Schrödinger equation generalized quadratic Yukawa potential and Hellman potential using analytical methods and we calculate eigenvalues, wave function and energy of the ground state these isotopes that it is agreement with experimental results. At last we resolve Klein-Gordon equation with potential Hellman and mass Depending on the location using the analytical NU method and calculate eigenvalues of energy and wave function.