The Laguerre pseudospectral method for the two-dimensional Schrodinger equation with symmetric nonseparable potentials

被引：3

作者：

Alici, Haydar ^{[1
]}

机构：

[1] Harran Univ, Dept Math, TR-63290 Sanliurfa, Turkey

来源：

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS | 2020年 / 49卷 / 02期

关键词：

the Laguerre pseudospectral method; two dimensional Schrodinger equation; symmetric potentials; SPECTRAL METHODS; INTERPOLATION; EIGENVALUES;

D O I：

10.15672/hujms.459593

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Hermite pseudospectral method is one of the natural techniques for the numerical treatment of the problems defined over unbounded domains such as two-dimensional time-independent Schrodinger equation on the whole real plane. However, it is shown here that for the symmetric potentials, transformation of the problem over the first quadrant and the application of the Laguerre pseudospectral method reduce the cost by a factor of four when compared to the Hermite pseudospectral method.

引用

页码：539 / 552

页数：14

共 50 条

[11] High-order implicit Galerkin-Legendre spectral method for the two-dimensional Schrodinger equation [J].

Liu, Wenjie ;

Wu, Boying .

APPLIED MATHEMATICS AND COMPUTATION, 2018, 324 :59-68

[12] Solution of Schrdinger Equation for Two-Dimensional Complex Quartic Potentials [J].

Ram Mehar Singh ;

Fakir Chand ;

SCMishra .

CommunicationsinTheoreticalPhysics, 2009, 51 (03) :397-406

[13] The eigenvalue gap for one-dimensional Schrodinger operators with symmetric potentials [J].

Huang, Min-Jei ;

Tsai, Tzong-Mo .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2009, 139 :359-366

[14] Analytic wave functions and energies for two-dimensional PT-symmetric quartic potentials [J].

Tichy, Vladimir ;

Skala, Lubomir .

CENTRAL EUROPEAN JOURNAL OF PHYSICS, 2010, 8 (04) :519-522

[15] Spherical harmonic-generalized Laguerre pseudospectral method for three-dimensional exterior problems [J].

Wang, Zhong-Qing ;

Zhang, Rong ;

Guo, Ben-Yu .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (09) :2123-2142

[16] A new kind of discretization scheme for solving a two-dimensional time-independent Schrodinger equation [J].

Wang, Zhongcheng ;

Shao, Hezhu .

COMPUTER PHYSICS COMMUNICATIONS, 2009, 180 (06) :842-849

[17] Finite difference approach for the two-dimensional Schrodinger equation with application to scission-neutron emission [J].

Rizea, M. ;

Ledoux, V. ;

Van Daele, M. ;

Vanden Berghe, G. ;

Carjan, N. .

COMPUTER PHYSICS COMMUNICATIONS, 2008, 179 (07) :466-478

[18] Numerical solution of the two-dimensional time independent Schrodinger equation with Numerov-type methods [J].

Kalogiratou, Z ;

Monovasilis, T ;

Simos, TE .

JOURNAL OF MATHEMATICAL CHEMISTRY, 2005, 37 (03) :271-279

[19] Pseudospectral solution of the two-dimensional Navier-Stokes equations in a disk [J].

Torres, DJ ;

Coutsias, EA .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1999, 21 (01) :378-403

[20] A Hermite pseudospectral solver for two-dimensional incompressible flows on infinite domains [J].

Yin, Zhaohua .

JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 258 :371-380

← 1 2 3 4 5 →