A new finite difference scheme with minimal phase-lag for the numerical solution of the Schrodinger equation

A new finite difference approach for the numerical solution of the eigenval ue problem of the Schrodinger equations is developed in this paper. The new approach is based on the maximization of the algebraic order and the minim ization of the phase-lag. We investigate two cases: (i) The specific case i n which the potential V(x) is an even function with respect to x. It is ass umed, also, that the wavefunctions tend to zero for x --> +/-infinity. (ii) The general case for positive and negative eigenvalues and for the well-kn own cases of the Morse potential and Woods-Saxon or Optical potential. Nume rical and theoretical results show that this new approach is more efficient when compared with previously derived methods. (C) 1999 Elsevier Science I nc. All rights reserved.