Solving quantum optimal control problems by wavelets method

We present the quantum equation and synthesize an optimal control proce dure for this equation. we develop a theoretical method for the analysis of quantum optimal control system given by the time depending schrödinger equation. the legendre wavelet method is proposed for solving this problem. this can be used as an efficient and accurate computational method for obtaining numerical solutions of different quantum optimal control problems. the distinguishing feature of this paper is that it makes the method, previously used to solve non-quantum control equations based on legendre wavelets, usable by using a change of variables for quantum control equations.