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Numerical Solution of the Schrodinger Equation in a Wavelet Basis for Hydrogen-Like Atoms

Patrick Fischer and Mireille Defranceschi
SIAM Journal on Numerical Analysis
Vol. 35, No. 1 (Feb., 1998), pp. 1-12
Stable URL: http://www.jstor.org/stable/2587090
Page Count: 12
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Numerical Solution of the Schrodinger Equation in a Wavelet Basis for Hydrogen-Like Atoms
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Abstract

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.

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