Solutions for One-Dimensional Time-Dependent Schrödinger Equations

Based on the finite difference scheme in time, the method of particular solutions using the radial basis functions is proposed to solve one-dimensional time-dependent Schrodinger equations. Two numerical examples with good accuracy are given to validate the proposed method.

[1]  Martin D. Buhmann,et al.  Radial Basis Functions , 2021, Encyclopedia of Mathematical Geosciences.

[2]  YuanTong Gu,et al.  Boundary meshfree methods based on the boundary point interpolation methods , 2002 .

[3]  Shmuel Rippa,et al.  An algorithm for selecting a good value for the parameter c in radial basis function interpolation , 1999, Adv. Comput. Math..

[4]  K. Atkinson The Numerical Evaluation of Particular Solutions for Poisson's Equation , 1985 .

[5]  Christophe Besse,et al.  Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation , 2003 .

[6]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[7]  C. S. Chen,et al.  A boundary meshless method using Chebyshev interpolation and trigonometric basis function for solving heat conduction problems , 2008 .

[8]  Xiaonan Wu,et al.  Analysis of finite element method for one-dimensional time-dependent Schrödinger equation on unbounded domain , 2008 .

[9]  J. Wertz,et al.  The role of the multiquadric shape parameters in solving elliptic partial differential equations , 2006, Comput. Math. Appl..

[10]  Xin Li,et al.  Trefftz Methods for Time Dependent Partial Differential Equations , 2004 .

[11]  A. Cheng Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions , 2000 .

[12]  Xiaonan Wu,et al.  A finite-difference method for the one-dimensional time-dependent schrödinger equation on unbounded domain , 2005 .