Perturbation theory for a nonlinear two-level system

Perturbation theory is an important tool in quantum mechanics, it can help to find solutions to the Schroedinger equation and has been proven to be a good approximation for linear quantum systems. In this paper, we examine whether the perturbation theory is available for nonlinear systems by exemplifying a nonlinear two-level system. The results show that the ratio (r) of the nonlinear rate C to the tunneling coefficient V determines the validity of the perturbation theory. For small ratio r, the perturbation theory is available; otherwise, it yields wrong results.