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Computation of the eigenvalues of the Schrödinger equation by exponentially-fitted Runge-Kutta-Nyström methods |
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| Authors: | Z Kalogiratou TE Simos |
| Affiliation: | a Department of Informatics and Computer Technology, Technological Educational Institution of Western Macedonia at Kastoria, Kastoria, P.O. Box 30, 52100 Greece b Department of International Trade, Technological Educational Institution of Western Macedonia at Kastoria, Kastoria, P.O. Box 30, 52100 Greece c Department of Computer Science and Technology, Faculty of Science and Technology, University of Peloponnessos, Greece |
| Abstract: | In this work 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∈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. |
| Keywords: | 02 60 Cb 02 60 Jh 02 70 Bf |
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