Solving quantum eigenvalue problems by discrete singular convolution

This paper explores the utility of a discrete singular convolution (DSC) algorithm for solving the Schrödinger equation. DSC kernels of Shannon, Dirichlet, modified Dirichlet and de la Vallée Poussin are selected to illustrate the present algorithm for obtaining eigenfunctions and eigenvalues. Four benchmark physical problems are employed to test numerical accuracy and speed of convergence of the present approach. Numerical results indicate that the present approach is efficient and reliable for solving the Schrödinger equation.