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Chebyshev expansions for wave functions

✍ Scribed by V.B. Sheorey

Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
755 KB
Volume
7
Category
Article
ISSN
0010-4655

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✦ Synopsis

Chebyshev series expansion of solutions of linear differential equations which occur in atomic scattering problems is discussed. We apply this technique to obtain both the regular and the irregular radial Coulomb wave functions. The Chebyshev expansion technique is extended to evaluate linearly independent solutions for the modified Coulomb potential. It is further shown that relativistic Coulomb wave functions may also be evaluated using Chebyshev expansion techniques.

An advantage of this technique is that wave functions and their derivatives can be represented to a very high accuracy in terms of only a small number of Chebyshev expansion coefficients over a wide range of values of the independent variable. Moreover, in certain cases it is possible to evaluate matrix elements involving functions so represented by using properties of Chebyshev polynomials and thus avoiding numerical integration altogether.

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