A time-varying quadratic function is selected as a target function. The Schrodinger equation of quantum systems is used to study the trajectory tracking. A error square Lyapunov function is selected based on the Lyapunov stability theorem to design control laws, so that realize tracking the target function from any initial state. System simulation experiments and the performances comparisons are studied under the Matlab with different initial states, which analyze the effects of initial states and observation to the system tracking performance, and verify the superiority of the proposed control laws tracking the target function.