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CP methods and the evaluation of negative energy Coulomb Whittaker functions. (English) Zbl 1074.65077
Summary: The CP (constant reference potential perturbation) methods are specialized methods for the solution of Schrödinger equations. They allow big step sizes and are well suited for oscillatory problems. As an illustration of the power of these methods, oscillating Whittaker functions of the second kind are obtained with high accuracy, using a high-order CP-method.

65L05 Numerical methods for initial value problems
34A30 Linear ordinary differential equations and systems, general
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
Full Text: DOI
[1] Abramowitz, M.; Stegun, I.A., Handbook of mathematical functions, (1965), Dover New York · Zbl 0515.33001
[2] Ixaru, L.Gr., Numerical methods for differential equations and applications, (1984), Reidel Dordrecht, Boston, Lancaster · Zbl 0301.34010
[3] Ixaru, L.Gr., CP methods for the Schrödinger equation, J. comput. appl. math., 125, 347-357, (2000) · Zbl 0971.65067
[4] Ixaru, L.Gr.; De Meyer, H.; Vanden Berghe, G., CP methods for the Schrödinger equation, revisited, J. comput. appl. math., 88, 289-314, (1997) · Zbl 0909.65045
[5] Ixaru, L.Gr.; De Meyer, H.; Vanden Berghe, G., SLCPM12—a program for solving regular sturm – liouville problems, Comput. phys. comm., 118, 259-277, (1999) · Zbl 1008.34016
[6] Ixaru, L.Gr.; De Meyer, H.; Vanden Berghe, G., Highly accurate eigenvalues for the distorted Coulomb potential, Phys. rev. E, 61, 3151-3159, (2000)
[7] Ixaru, L.Gr.; Rizea, M., A numerov-like scheme for the numerical solution of the Schrödinger equation in the deep continuum spectrum of energies, Comput. phys. comm., 19, 23-27, (1980)
[8] Ledoux, V.; Van Daele, M.; Vanden Berghe, G., CP methods of higher order for sturm – liouville and Schrödinger equations, Comput. phys. commun., 162, 151-165, (2004) · Zbl 1196.65131
[9] V. Ledoux, M. Van Daele, G. Vanden Berghe, MATSLISE: A MATLAB package for the numerical solution of Sturm-Liouville and Schrödinger equations, ACM Trans. Math. Software 2004, submitted for publication. · Zbl 1136.65327
[10] Noble, C.J., Evaluation of negative energy Coulomb Whittaker functions, Comput. phys. comm., 159, 55-62, (2004)
[11] Seaton, M.J., NUMER, a code for numerov integrations of Coulomb functions, Comput. phys. comm., 146, 254-260, (2002) · Zbl 1007.81022
[12] Simos, T.E., A simple accurate method for the numerical solution of the schrodinger equation, Helv. phys. acta, 70, 781, (1997) · Zbl 0892.65046
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