A New Methodology for the Development of Numerical Methods for the   Numerical Solution of the Schr\"odinger Equation
  In the present paper we introduce a new methodology for the construction of numerical methods for the approximate solution of the one-dimensional Schr\"odinger equation. The new methodology is based on the requirement of vanishing the phase-lag and its derivatives. The efficiency of the new methodology is proved via error analysis and numerical applications. 
Z.A. Anastassi, D.S. Vlachos, T.E. Simos