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Computation of the eigenvalues of the Schrödinger equation by exponentially-fitted Runge-Kutta-Nyström methods. (English) Zbl 1198.81088

Summary: We consider exponentially fitted and trigonometrically fitted Runge-Kutta-Nyström methods. These methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions \(\exp(wx), \exp( - wx)\), or \(\sin(wx), \cos(wx), w\in\mathbb{R}\). We modify existing RKN methods of fifth and sixth order. We apply these methods to the computation of the eigenvalues of the Schrödinger equation with different potentials as the harmonic oscillator, the doubly anharmonic oscillator and the exponential potential.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

Software:

Mathematica
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Full Text: DOI

References:

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