Numerical Solution of the Schrödinger Equation in a Wavelet Basis for Hydrogen-like Atoms

Abstract

An iterative method is proposed to solve the Schrödinger eigenvalue problem in a wavelet framework. Orthonormal wavelets are used to represent the corresponding operator as a sparse band matrix. This representation, called the nonstandard (NS) form, is obtained by means of the Beylkin--Coifman--Rokhlin (BCR) algorithm and simplifies the numerical calculations. Problems due to the one-dimensional mathematical model and to the discretization process receive special attention.