A new effective algorithm for the resonant state of a Schrdinger equation
In this paper we present a new effective algorithm for the Schrdinger equation. This new method differs from the original Numerov method only in one simple coefficient, by which we can extend the interval of periodicity from 6 to infinity and obtain an embedded correct factor to improve the accuracy. We compare the new method with the original Numerov method by the well-known problem of WoodsSaxon potential. The numerical results show that the new method has great advantage in accuracy over the original. Particularly for the resonant state, the accuracy is improved with four orders overall, and even six to seven orders for the highest oscillatory solution. Surely, this method will replace the original Numerov method and be widely used in various area.
schrdinger equation numerov method trigonometric fitting p-stable high-oscillatory solution