Coulomb wave equation

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1: 33.2 Definitions and Basic Properties

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§33.2(i) Coulomb Wave Equation

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2: 33.14 Definitions and Basic Properties

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§33.14(i) Coulomb Wave Equation

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3: 33.22 Particle Scattering and Atomic and Molecular Spectra

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§33.22(vi) Solutions Inside the Turning Point

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4: 30.12 Generalized and Coulomb Spheroidal Functions

… ►Generalized spheroidal wave functions and Coulomb spheroidal functions are solutions of the differential equation …

5: 18.39 Applications in the Physical Sciences

… ►(where the minus sign is often omitted, as it arises as an arbitrary phase when taking the square root of the real, positive, norm of the wave function), allowing equation (18.39.37) to be rewritten in terms of the associated Coulomb–Laguerre polynomials ${𝐋}_{n+l}^{2l+1}({\rho }_n)$. … ►

Discretized and Continuum Expansions of Scattering Eigenfunctions in terms of Pollaczek Polynomials: J-matrix Theory

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6: 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. …

7: Bibliography F

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The Lamé wave equation. Uspekhi Mat. Nauk 44 (1(265)), pp. 123–144, 248 (Russian).

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Notes:

In Russian. English translation: Russian Math. Surveys, 44(1989), no. 1, pp. 153–180

External Links:

ISSN 0042-1316, Document, MathReview (R. G. Langebartel), ZentralBlatt

Referenced by:

§29.11.

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Spheroidal Wave Functions. Stanford University Press, Stanford, CA.

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External Links:

MathReview (J. C. P. Miller), ZentralBlatt

Referenced by:

§30.1, §30.10, 2nd item, Ch.30.

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Electromagnetic Diffraction and Propagation Problems. International Series of Monographs on Electromagnetic Waves, Vol. 1, Pergamon Press, Oxford.

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External Links:

MathReview (R. F. Millar)

Referenced by:

§9.16.

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Diffraction of radio waves around the earth’s surface. Acad. Sci. USSR. J. Phys. 9, pp. 255–266.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§9.1, Notations U, Notations V.

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Numerical treatment of Coulomb wave functions. Rev. Mod. Phys. 27 (4), pp. 399–411.

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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§33.10(ii), §33.11, §33.12(i), §33.9(ii).

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8: Bibliography H

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Calculation of Coulomb wave functions for high energies. Phys. Rev. 54 (8), pp. 627–628.

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External Links:

Document

Referenced by:

§33.7.

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Coulomb Wave Functions. In Handbuch der Physik, Bd. 41/1, S. Flügge (Ed.), pp. 408–465.

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External Links:

MathReview (G. Källén)

Referenced by:

§33.2(iii), §33.23(vii), §33.23(vii), §33.24, §33.5(ii), §33.7, Ch.33.

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Analytical structure and properties of Coulomb wave functions for real and complex energies. Ann. Physics 155 (2), pp. 461–493.

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External Links:

ISSN 0003-4916, Document, MathReview

Referenced by:

§33.10(ii), §33.13, §33.22(vii).

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Bessel function expansions of Coulomb wave functions. J. Math. Phys. 26 (4), pp. 656–659.

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External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§33.10(ii), §33.10(iii), §33.14(iv), §33.9(ii), §33.9(ii).

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The eigenvalues of the angular spheroidal wave equation. Stud. Appl. Math. 66 (3), pp. 217–240.

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External Links:

ISSN 0022-2526, MathReview, ZentralBlatt

Referenced by:

§30.9(iii).

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9: Software Index

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	Open Source													With Book						Commercial
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28 Mathieu Functions and Hill’s Equation
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30 Spheroidal Wave Functions
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30.18(iii) Wave Functions														✓			✓		✓			✓			Van Buren
33 Coulomb Functions
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10: Bibliography N

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Scattering theory of waves and particles. Dover Publications, Inc., Mineola, NY.

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Notes:

Reprint of the 1982 second edition [Springer, New York; MR0666397 (84f:81001)], with list of errata prepared for this edition by the author

External Links:

ISBN 0-486-42535-5, MathReview Entry

Referenced by:

§1.18(vi), §1.18(viii).

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Coulomb Functions for Large Values of the Parameter $\eta$ . Technical report Atomic Energy of Canada Limited, Chalk River, Ontario.

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Notes:

Rep. CRT-526

External Links:

MathReview (A. Erdélyi)

Referenced by:

§33.7.

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COULN, a program for evaluating negative energy Coulomb functions. Comput. Phys. Comm. 33 (4), pp. 413–419.

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Notes:

Double-precision Fortran code.

External Links:

Document, Code

Referenced by:

2nd item, 7th item.

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Evaluation of negative energy Coulomb (Whittaker) functions. Comput. Phys. Comm. 159 (1), pp. 55–62.

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Notes:

Double-precision Fortran-90 code.

External Links:

Document, Code

Referenced by:

§33.23(vi), 8th item.

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Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations. Institute of Physics Publishing, Bristol.

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External Links:

ISBN 0-7503-0610-6, MathReview (Peter Giblin), ZentralBlatt

Referenced by:

§36.14(ii).

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