Double exponential Sinc numerical methods for the two-dimensional time-independent Schrödinger equation

Abstract

ABSTRACT In this work, the Sinc collocation and Sinc–Galerkin methods are applied in conjunction with double exponential transformations to solve the two-dimensional time-independent Schrödinger equation. The block centrosymmetry is introduced as a two-dimensional extension of the well-known centrosymmetric property. It helps to significantly reduce the computational time while calculating the eigenvalues of the system matrices. Numerical examples with a variety of separable and nonseparable potential functions are presented. A comparison between the single and double exponential Sinc methods confirms the efficiency and superiority of the double exponential Sinc methods.