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A finite-difference method for the numerical solution of the Schrödinger equation. (English) Zbl 0877.65054

New finite difference methods are proposed for the numerical solution of the Schrödinger equation: \(y''(x)= [V(x)- E]y(x)\), where the potential \(V\) is a given function and \(E\) a real constant. The methods are symmetric four-step linear methods for special second-order equations whose coefficients have been suitably selected (for some type of potentials) taking into account not only the local discretization error but also the phase-lag and the interval of periodicity. In this way, the authors propose as optimal a sixth-order method with phase-lag of order eight.
The paper includes also the results of some numerical experiments with different potentials in which to show the efficiency of the new method it is compared to an extended Numerov’s method proposed by V. Fack and G. Vanden Berghe [J. Phys. A 20, 4153-4160 (1987; Zbl 0626.65079)].
Reviewer: M.Calvo (Zaragoza)

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)

Citations:

Zbl 0626.65079
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References:

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