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

An iterative method is proposed to solve the Schrodinger 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.

[1]  A three‐dimensional finite element approach towards molecular SCF computations , 1992 .

[2]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[3]  F. Chatelin.  Valeurs propres de matrices , 1988 .

[4]  J. Olsen,et al.  Large MCHF calculations on the electron affinity of boron , 1990 .

[5]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[6]  R. Coifman,et al.  Fast wavelet transforms and numerical algorithms I , 1991 .

[7]  T. F. Jordan.  Conditions on wave functions derived from operator domains , 1976 .

[8]  Joseph Delhalle,et al.  Numerical determination of the electronic structure of atoms, diatomic and polyatomic molecules , 1989 .

[9]  A. Thakkar,et al.  Linear integrability of wave functions , 1988 .

[10]  Representation of the Atomic Hartree-Fock Equations in a Wavelet Basis by Means of the BCR Algorithm , 1994 .

[11]  M. Defranceschi,et al.  Electronic structure of H2 and HeH+ computed directly in momentum space , 1993 .

[12]  One-Dimensional Hydrogen Atom , 1959 .

[13]  J. Antoine,et al.  Wavelet-like orthonormal bases for the lowest Landau level , 1994 .

[14]  Cho,et al.  Wavelets in electronic structure calculations. , 1993, Physical review letters.

[15]  M. Defranceschi,et al.  Looking at atomic orbitals through fourier and wavelet transforms , 1993 .

[16]  M. Defranceschi,et al.  Electronic structure of Li− and F− calculated directly in momentum space , 1993 .

[17]  M. Defranceschi,et al.  Molecular Hartree-Fock equations for iteration-variation calculations in momentum space , 1992 .

[18]  R. Mcweeny,et al.  Methods Of Molecular Quantum Mechanics , 1969 .

[19]  André D. Bandrauk,et al.  Molecules in Laser Fields , 1995 .