A finite-difference method for the numerical solution of the Schrِdinger equation

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