An explicit eighth order method with minimal phase-lag for the numerical solution of the Schrodinger equation

A new explicit hybrid eighth algebraic order two-step method with phase-lag of order twelve is developed for computing eigenvalues and resonances of the one-dimensional Schrodinger equation. Based on this new method and on the method developed recently by Simos we obtain a new variable-step procedure for the numerical integration of the Schrodinger equation, Numerical results obtained for the integration of the resonance problem for the well known case of the Woods-Saxon potential and for the integration of the eigenvalue problem for the well known case of the Morse potential show that this new method is better than other variable step methods. (C) 1997 Elsevier Science B.V.