An extended numerov-type method for the numerical solution of the Schrödinger equation

A new method, which is based on the new property of phase-lag, for computing eigenvalues of Schrödinger equations with potentials is developed in this paper. We investigate two cases. 1. (i) The specific case in which the potential V(x) is an even function with respect to x. It is assumed, also, that the wavefunctions tend to zero for x → ±∞. 2. (ii) The general case for positive and negative eigenvalues and for the well-known cases of the Morse potential and of the Woods-Saxon or Optical potential. Numerical and theoretical results show that this new method is more efficient compared with previously derived methods.