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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. 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:
81Q05Closed and approximate solutions to quantum-mechanical equations
65L15Eigenvalue problems for ODE (numerical methods)
65L06Multistep, Runge-Kutta, and extrapolation methods
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