Representation of solutions to the one-dimensional Schrodinger equation in terms of Neumann series of Bessel functions

被引：33
|
作者：
Kravchenko, Vladislav V. [1 ]
Navarro, Luis J. [2 ]
Torba, Sergii M. [1 ]
机构：
[1] CINVESTAV, IPN, Dept Math, Unidad Queretaro, Libramiento Norponiente 2000, Queretaro 76230, Qro, Mexico
[2] Univ Simon Bolivar, Dept Pure & Appl Math, Caracas 1080A, Venezuela
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2017年 / 314卷
关键词：
Sturm-Liouville problem; Transmutation operator; One dimensional Schrodinger equation; Neumann series of Bessel functions; Fourier-Legendre series; Numerical solution of spectral problems; STURM-LIOUVILLE PROBLEMS; PARAMETER POWER-SERIES; SINGULAR POTENTIALS; SPECTRAL PROBLEMS; OPERATORS; TRANSMUTATIONS; APPROXIMATION; TRANSFORMATION; EXPANSION; PACKAGE;
D O I：
10.1016/j.amc.2017.07.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A new representation of solutions to the equation y" + q(x)y = omega(2)y is obtained. For every x the solution is represented as a Neumann series of Bessel functions depending on the spectral parameter omega. Due to the fact that the representation is obtained using the corresponding transmutation operator, a partial sum of the series approximates the solution uniformly with respect to omega which makes it especially convenient for the approximate solution of spectral problems. The numerical method based on the proposed approach allows one to compute large sets of eigendata with a nondeteriorating accuracy. (C) 2017 Elsevier Inc. All rights reserved.
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页码：173 / 192
页数：20
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