In the present paper, an initial boundary value problem for the linear Schrodinger equation including the momentum operator ¨ is introduced. This problem is discretized by the finite difference method and a difference scheme is presented. Moreover, an estimate for the solution of the proposed scheme is obtained. Finally, with the help of the estimate, it is proved that the proposed scheme is unconditionally stable and convergent. In the present paper, an initial boundary value problem for the linear Schrodinger equation including the momentum operator ¨ is introduced. This problem is discretized by the finite difference method and a difference scheme is presented. Moreover, an estimate for the solution of the proposed scheme is obtained. Finally, with the help of the estimate, it is proved that the proposed scheme is unconditionally stable and convergent.