The variation of the expectation matrix of position and momentum operator in time can serve us to investigate the evolution of a quantum system in time. This brings the utilization of the ODEs instead of Schrodinger's equation at the expense of incapability for the calculation of the wave function. As long as we deal with the observables which can be expressed in terms of position and momentum operators this may be quite practical to know about the quantum dynamics of the system under consideration. Expectation matrix of an operator becomes a function of the expectation matrices of the position and momentum operator when the fluctuations diminish to zero. At this limit, the time-variant ODEs for the expectation matrices of the position and momentum operator can be handled by using the matrix algebraic tools even in the case of nonlinearities in the potential function. This work presents certain details about these points.