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A family of hybrid, exponentially fitted, predictor-corrector methods is developed for the numerical integration of the one-dimensional Schr6dinger equation. The formula considered contains certain free parameters which allow it to be fitted automatically to exponential functions. The new methods are of algebraic order six, they are very simple and integrate more exponential functions than both the well-known fourth-order Numerov-type exponentially fitted methods and the Runge-Kutta-typedoi:10.1016/s0377-0427(97)00188-x fatcat:oglh2nrkqvfsdflibupebprdky