Sinc-Integral method to solve the linear Schrodinger equation

Document Type : Original Article


1 Department of Mathematics, Qom University of Technology, Qom, Iran

2 Department of Mathematics, Qom University of Technology


The integral equation method is presented to solve the linear Schrodinger equation and obtain the eigenvalues. The eigenvalues obtained through this method are compared with Sinc-Collocation method. We show that our method is more accurate than Sinc-Collocation method.
Some properties of the Sinc methods required for our subsequent development are given and utilized. Numerical examples are included to demonstrate the validity and applicability of the presented techniques.


[1] S.M.A. Aleomraninejada, M. solaimani, Electronic spectrum of linear Schrodinger equations with some potentials by Sinc-Galerkin and Sinc-Collocation methods, submitted.
[2] S.M.A. Aleomraninejada, M. solaimani, Numerical solution of some non-linear eigenvalue differential equations by finite difference-self consistent, Mathematical Analysis and Convex Optimization, 1(1) 2020, 57-64.
[3] S.M.A. Aleomraninejad, M. Solaimani, M. Mohsenizadeh, L. Lavaei, Discretized Euler-Lagrange Variational Study of Nonlinear Optical Recti cation Coefficients, Physica Scripta, 93(9) 2018, 095803.
[4] A.K. Alomari, M.S.M. Noorani, R. Nazar, Explicit series solutions of some linear and nonlinear Schrodinger equations via the homotopy analysis method, Communications in Nonlinear Science and Numerical Simulation, 14(4) 2009, 1196-1207.
[5] A.R. Amani, M.A. Moghrimoazzen, H. Ghorbanpour, S. Barzegaran, The ladder operators of Rosen Morse Potential with Centrifugal term by Factorization Method, African Journal of Mathematical Physics, (10) 2011, 31-37.
[6] C.B. Compean, M. Kirchbach, The trigonometric RosenMorse potential in the supersymmetric quantum mechanics and its exact solutions, Journal of Physics A: Mathematical and General, 39(3) 2005, 547.
[7] M. Dehghan, F. Emami-Naeini, Solving the two-dimensional Schrodinger equation with nonhomogeneous boundary conditions, Applied Mathematical Modelling, 37(22) 2013, 9379-9397.
[8] M. Dehghan, A. Saadatmandi, The numerical solution of a nonlinear system of second-order boundary value problems using the sinc-collocation method, Mathematical and Computer Modelling, 46(11) 2007, 1434-1441.
[9] M. El-Gamel, Sinc-collocation method for solving linear and nonlinear system of second-order boundary value problems, Applied Mathematics, 3(11) 2012, 1627-1633.
[10] S.M. Ikhdair, M. Hamzavi, R. Sever, Spectra of cylindrical quantum dots: The effect of electrical and magnetic fields together with AB flux field, Physica B: Condensed Matter, 407(23) 2012, 4523-4529.
[11] A.M. Ishkhanyan, Exact solution of the Schrodinger equation for the inverse square root potential V0/x, Europhysics Letters, 112(1) 2015, 10006.
[12] A. Niknam, A.A. Rajabi, M. Solaiman, Solutions of D-dimensional Schrodinger equation for Woods Saxon potential with spin-orbit, coulomb and centrifugal terms through a new hybrid numerical fitting Nikiforov-Uvarov method, J Theor Appl Phys, 10(1) 2016, 53-59.
[13] T. Okayama, T. Matsuo, M. Sugihara, Error estimates with explicit constants for Sinc approximation, Sinc quadrature, and Sinc inde nite integration, Numerische Mathematik, 124(2) 2013, 361-394.
[14] M. Solaimani, S.M.A. Aleomraninejad, L. Leila, Optical recti cation in quantum wells within different confinement and nonlinearity regimes, Superlattices and Microstructures, (111) 2017, 556-567.
[15] F. Stenger, Approximations via Whittaker's Cardinal Function, Journal of Approximation Theory, 17(3) 1976, 222-240.
[16] F. Stenger, Numerical Methods Based on Sinc and Analytic Functions, Springer, Berlin, New York, 1993.
[17] G. Xue, E. Yuzbasi, Fixed point theorems for solutions of the stationary Schrodinger equation on cones, Fixed Point Theory and Applications, 2015(1) 2015, 1-11.