In this paper, we present the new class of six-step P-stable multiderivative methods of eighth (and tenth) algebraic order with vanishing phase-lag and its first, second, third, fourth (and fifth) derivatives for the numerical integration of the one-dimensional Schrodinger equation. We perform an analysis of the local truncation error of the methods for the general and special cases of the Schrödinger equation, where we show the decrease of the maximum power of the energy in relation to the corresponding classical methods. For the produced methods we investigate their errors and stability. Based on the above mentioned analysis we give some remarks and conclusions about their efficacy in the numerical integration of the radial Schrödinger equation.
