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1: William P. Reinhardt

… ►Older work on the scattering theory of the atomic Coulomb problem led to the discovery of new classes of orthogonal polynomials relating to the spectral theory of Schrödinger operators, and new uses of old ones: this work was strongly motivated by his original ownership of a 1964 hard copy printing of the original AMS 55 NBS Handbook of Mathematical Functions. …

2: 18.39 Applications in the Physical Sciences

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§18.39(ii) A 3D Separable Quantum System, the Hydrogen Atom

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The Quantum Coulomb Problem

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The Relativistic Quantum Coulomb Problem

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The Quantum Coulomb Problem: Scattering States

►The positive energy (scattering) eigenfunctions for the above Coulomb problem, with potential $V(r)=-Z{e}^2/r$ are discussed in Chapter 33 for each integer $l$. …

3: 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). … ►

4: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►In unusual cases $N=\mathrm{\infty }$, even for all $\mathrm{\ell }$, such as in the case of the Schrödinger–Coulomb problem ($V=-r^{-1}$) discussed in §18.39 and §33.14, where the point spectrum actually accumulates at the onset of the continuum at $\lambda =0$, implying an essential singularity, as well as a branch point, in matrix elements of the resolvent, (1.18.66). … …

5: 18.35 Pollaczek Polynomials

… ►These polynomials also occur in connection with the Coulomb problem, see §18.39(iv).

6: 17.17 Physical Applications

… ►It involves $q$-generalizations of exponentials and Laguerre polynomials, and has been applied to the problems of the harmonic oscillator and Coulomb potentials. …

7: Bibliography B

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Problem of two Coulomb centres at large intercentre separation: Asymptotic expansions from analytical solutions of the Heun equation. J. Phys. A 30 (2), pp. 559–571.

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External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§31.13.

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8: Bibliography H

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Solving Ordinary Differential Equations. I. Nonstiff Problems. 2nd edition, Springer Series in Computational Mathematics, Vol. 8, Springer-Verlag, Berlin.

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Notes:

A reprinting with corrections appeared in 2000.

External Links:

ISBN 3-540-56670-8, MathReview, ZentralBlatt

Referenced by:

§3.7(v), §3.7(i).

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Solving Ordinary Differential Equations. I. Nonstiff Problems. 2nd edition, Springer-Verlag, Berlin.

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External Links:

ISBN 3-540-56670-8, Document, MathReview

Referenced by:

§32.17.

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Some problems of “Partitio Numerorum” (VI): Further researches in Waring’s Problem. Math. Z. 23, pp. 1–37.

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Notes:

Reprinted in Collected Papers of G. H. Hardy (Including Joint papers with J. E. Littlewood and others), Vol. I, pp. 469–505, Clarendon Press, Oxford, 1966.

External Links:

ISSN 0025-5874, Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.13(iii).

Encodings:

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Two-center Coulomb functions. Comput. Phys. Comm. 103 (2-3), pp. 209–216.

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Notes:

Double-precision Fortran code.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

6th item.

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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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9: Bibliography C

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On the expansion of a Coulomb potential in spherical harmonics. Proc. Cambridge Philos. Soc. 46, pp. 626–633.

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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§34.12.

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A moment problem and a family of integral evaluations. Trans. Amer. Math. Soc. 358 (9), pp. 4071–4097.

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External Links:

ISSN 0002-9947, Document, MathReview (Roelof Koekoek), ZentralBlatt

Referenced by:

§18.28(iv).

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CRCWFN: Coupled real Coulomb wavefunctions. Comput. Phys. Comm. 79 (1), pp. 143–155.

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Notes:

Double-precision Fortran code.

External Links:

ISSN 0010-4655, Document, Code, ZentralBlatt

Referenced by:

5th item.

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Coulomb phase shift. American Journal of Physics 47 (8), pp. 683–684.

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External Links:

Document

Referenced by:

§5.20.

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Some non-central distribution problems in multivariate analysis. Ann. Math. Statist. 34 (4), pp. 1270–1285.

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External Links:

FullText, MathReview (I. Olkin), ZentralBlatt

Referenced by:

§35.4(i), §35.4(ii).

Encodings:

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10: Bibliography K

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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.

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External Links:

ISSN 0266-5611, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.11(iv).

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An improvement of the remainder term in the divisor problem. Mat. Zametki 6, pp. 545–554 (Russian).

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Notes:

In Russian. English translation: Math. Notes 6(1969), no. 5, pp. 784–791.

External Links:

Document, MathReview (A. I. Vinogradov), ZentralBlatt

Referenced by:

§27.11, Erratum (V1.1.8) for Section 27.11.

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Sferoidalnye i kulonovskie sferoidalnye funktsii. Izdat. “Nauka”, Moscow (Russian).

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Notes:

Translated title: Spheroidal and Coulomb Spheroidal Functions

External Links:

MathReview

Referenced by:

§30.12, Ch.30, §31.13.

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Basic Methods in Transfer Problems. Radiative Equilibrium and Neutron Diffusion. Oxford University Press, Oxford.

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Notes:

With the collaboration of I. W. Busbridge

External Links:

MathReview (S. Chandrasekhar), ZentralBlatt

Referenced by:

§8.19(x), §8.24(iii).

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Sur le problème de la rotation d’un corps solide autour d’un point fixe. Acta Math. 12 (1), pp. 177–232 (French).

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External Links:

ISSN 0001-5962, Document, MathReview Entry, ZentralBlatt

Referenced by:

§22.19(iv).

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