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[Licence| Download | New Version Template] adtt_v1_0.tar.gz(44 Kbytes) | ||
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Manuscript Title: A Mathematica program for the two-step twelfth-order method with multi-derivative for the numerical solution of a one-dimensional Schrödinger equation | ||

Authors: Z. Wang, Y. Ge, Y. Dai, D. Zhao | ||

Program title: ShdEq.nb | ||

Catalogue identifier: ADTT_v1_0Distribution format: tar.gz | ||

Journal reference: Comput. Phys. Commun. 160(2004)23 | ||

Programming language: Mathematica 4.2. | ||

Computer: The program has been designed for the microcomputer and been tested on the microcomputer. | ||

Operating system: Windows XP. | ||

RAM: 51 712 bytes | ||

Keywords: Multi-derivative method, High-order linear two-step methods, Schrödinger equation, Eigenvalue problems, High precision methods, Numerov's method. | ||

PACS: 02.60.Cb, 02.70.Bf. | ||

Classification: 4.3. | ||

Nature of problem:Numerical integration of one-dimensional or radial Schrödinger equation to find the eigenvalues for a bound states and phase shift for a continuum state. | ||

Solution method:Using a two-step method twelfth-order method to integrate a Schrödinger equation numerically from both two ends and the connecting conditions at the matching point, an eigenvalue for a bound state or a resonant state with a given phase shift can be found. | ||

Restrictions:The analytic form of the potential function and its high-order derivatives must be known. | ||

Unusual features:Take advantage of the high-order derivatives of the potential function and efficient algorithm, the program can provide all the numerical solution of a given Schrödinger equation, either a bound or a resonant state, with a very high precision and within a very short CPU time. The program can apply to a very broad range of problems because the method has a very large interval of periodicity. | ||

Running time:Less than one second. | ||

References: | ||

[1] | T.E. Simos, Proc. Roy. Soc. London A 441 (1993) 283. | |

[2] | Z. Wang, Y. Dai, An eighth-order two-step formula for the numerical integration of the one-dimensional Schrödinger equation, Numer. Math. J. Chinese Univ. 12 (2003) 146. | |

[3] | Z. Wang, Y. Dai, An twelfth-order four-step formula for the numerical integration of the one-dimensional Schrödinger equation, Internat. J. Modern Phys. C 14 (2003) 1087. |

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