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

A new finite difference approach for the numerical solution of the eigenvalue problem of the Schrodinger equations is developed in this paper. The new approach is based on the maximization of the algebraic order and the minimization of the phase-lag. 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 wavefunctions tend to zero for x->+/-~. (ii) The general case for positive and negative eigenvalues and for the well-known cases of the Morse potential and Woods-Saxon or Optical potential. Numerical and theoretical results show that this new approach is more efficient when compared with previously derived methods.

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