Coulomb wave functions

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11: Bibliography D

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Coulomb wave functions with complex values of the variable and the parameters. J. Math. Phys. 40 (12), pp. 6145–6166.

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External Links:

ISSN 0022-2488, Document, MathReview (Raj Wilson), ZentralBlatt

Referenced by:

§33.13.

Encodings:

BibTeX

12: 33.2 Definitions and Basic Properties

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§33.2(i) Coulomb Wave Equation

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13: Bibliography B

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Coulomb wave functions for all real $\eta$ and $\rho$ . Comput. Phys. Comm. 8 (5), pp. 377–395.

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Notes:

Single-precision Fortran code for positive energies. For modification see same journal, 11(1976), p. 141.

External Links:

Document, Code

Referenced by:

§3.10(iii), §33.26(ii), §33.8.

Encodings:

BibTeX

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Methods of calculation of radial wave functions and new tables of Coulomb functions. Physical Rev. (2) 80, pp. 553–560.

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External Links:

Document, MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§33.7.

Encodings:

BibTeX

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14: Bibliography C

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Coulomb Wave Functions. Roy. Soc. Math. Tables, Vol. 11, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-06156-3, MathReview (John Todd), ZentralBlatt

Referenced by:

item Curtis (1964a):, §33.14(i), §33.20(iv), §33.21(ii), §33.23(vi), 2nd item, §33.9(ii), Notations P, Notations Q.

Encodings:

BibTeX

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15: Bibliography M

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Precise Coulomb wave functions for a wide range of complex $\mathrm{\ell }$, $\eta$ and $z$ . Computer Physics Communications 176 (3), pp. 232–249.

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Notes:

C++ code. Maximum accuracy 10D

External Links:

Document, Code, ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

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16: 31.12 Confluent Forms of Heun’s Equation

… ►This has regular singularities at $z=0$ and $1$, and an irregular singularity of rank 1 at $z=\mathrm{\infty }$. ►Mathieu functions (Chapter 28), spheroidal wave functions (Chapter 30), and Coulomb spheroidal functions (§30.12) are special cases of solutions of the confluent Heun equation. …

17: Bibliography S

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FGH, a code for the calculation of Coulomb radial wave functions from series expansions. Comput. Phys. Comm. 146 (2), pp. 250–253.

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Notes:

Single-precision Fortran code.

External Links:

Document, Code, ZentralBlatt

Referenced by:

10th item.

Encodings:

BibTeX

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18: Software Index

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	Open Source													With Book						Commercial
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30 Spheroidal Wave Functions
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►‘✓’ indicates that a software package implements the functions in a section; ‘a’ indicates available functionality through optional or add-on packages; an empty space indicates no known support. … ►In the list below we identify four main sources of software for computing special functions. … ►

Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

… ►The following are web-based software repositories with significant holdings in the area of special functions. …

19: 33.14 Definitions and Basic Properties

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§33.14(i) Coulomb Wave Equation

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20: 33.22 Particle Scattering and Atomic and Molecular Spectra

… ►For scattering problems, the interior solution is then matched to a linear combination of a pair of Coulomb functions, $F_{\mathrm{\ell }}(\eta ,\rho )$ and $G_{\mathrm{\ell }}(\eta ,\rho )$, or $f(ϵ,\mathrm{\ell };r)$ and $h(ϵ,\mathrm{\ell };r)$, to determine the scattering $S$-matrix and also the correct normalization of the interior wave solutions; see Bloch et al. (1951). …