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11: 9.16 Physical Applications

… ►In the case of the rainbow, the scattering amplitude is expressed in terms of $\mathrm{Ai}\left(x\right)$, the analysis being similar to that given originally by Airy (1838) for the corresponding problem in optics. …

12: Bibliography C

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

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§18.28(iv).

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Inverse Acoustic and Electromagnetic Scattering Theory. 2nd edition, Applied Mathematical Sciences, Vol. 93, Springer-Verlag, Berlin.

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ISBN 3-540-62838-X, MathReview, ZentralBlatt

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§10.73(i).

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Calculation of angular distributions in complex angular momentum theories of elastic scattering. Molecular Physics 37 (6), pp. 1703–1712.

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Document

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§14.31(iii).

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

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FullText, MathReview (I. Olkin), ZentralBlatt

Referenced by:

§35.4(i), §35.4(ii).

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Constraints on the phase of scattering amplitudes due to positivity. Nuclear Phys. B 49, pp. 413–440.

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Document

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§18.39(v).

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13: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►this being a matrix element of the resolvent $F(T)={\left(z-T\right)}^{-1}$, this being a key quantity in many parts of physics and applied math, quantum scattering theory being a simple example, see Newton (2002, Ch. 7). … ►which appear in the quantum theory of binding or scattering of a particle in a spherically symmetric potential $V(r)$ in three dimensions, and where $r\in [0,\mathrm{\infty })$. The bound states are in the negative energy discrete spectrum, and the scattering states are in the positive energy continuous spectrum, ${𝝈}_c=[0,\mathrm{\infty })$, or, said more simply, in the continuum. … … ►See, in particular, the overview Everitt (2005b, pp. 45–74), and the uniformly annotated listing of $51$ solved Sturm–Liouville problems in Everitt (2005a, pp. 272–331), each with their limit point, or circle, boundary behaviors categorized.

14: 7.21 Physical Applications

… ►These applications include astrophysics, plasma diagnostics, neutron diffraction, laser spectroscopy, and surface scattering. …

15: Bibliography G

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Quasirandom distributed bases for bound problems. J. Chem. Phys. 114 (9), pp. 3929–3939.

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§18.39(iii).

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Elastic scattering of photons by a hydrogen atom. Phys. Rev. 163 (1), pp. 147–155.

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Document

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§15.18.

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Problem 72-21, Laplace transforms of Airy functions. SIAM Rev. 15 (4), pp. 796–798.

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Notes:

Problem proposed by P. Smith.

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Document

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(9.10.14), (9.10.15), (9.10.16), §9.10(v).

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New method for constructing wavefunctions for bound states and scattering. J. Chem. Phys. 51, pp. 14–25.

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Document, MathReview (K. J. Le Couteur)

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§9.11(iv), §9.17(iii).

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Stirling number representation problems. Proc. Amer. Math. Soc. 11 (3), pp. 447–451.

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FullText, MathReview (L. Carlitz), ZentralBlatt

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§26.1, §26.1, Notations S, Notations S.

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16: Bibliography

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Solitons, Nonlinear Evolution Equations and Inverse Scattering. London Mathematical Society Lecture Note Series, Vol. 149, Cambridge University Press, Cambridge.

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ISBN 0-521-38730-2, Document, Link, MathReview (Walter Oevel), ZentralBlatt

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§22.19(ii), §22.19(iii), §32.11(ii), §32.5, §9.16, Profile Mark J. Ablowitz, Profile Peter A. Clarkson.

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Solitons and the Inverse Scattering Transform. SIAM Studies in Applied Mathematics, Vol. 4, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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ISBN 0-89871-174-6, MathReview (Benno Fuchssteiner), ZentralBlatt

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§21.9, §21.9, §32.5, §9.16, Profile Mark J. Ablowitz.

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High-order interior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder. J. Opt. Soc. Amer. A 14 (6), pp. 1305–1315.

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FullText

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§36.14(ii).

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Unsteady lifting-line theory as a singular-perturbation problem. J. Fluid Mech 153, pp. 59–81.

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Document, ZentralBlatt

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§11.12.

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Scattering by singular potentials with a perturbation – Theoretical introduction to Mathieu functions. J. Mathematical Phys. 16, pp. 961–970.

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Erratum: same journal 17 (1975), no. 7, p. 1361

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Document, MathReview (K. Veselic), ZentralBlatt

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4th item.

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17: Bibliography K

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The Scattering of Light and Other Electromagnetic Radiation. Academic Press, New York.

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ISBN 0-12-404550-2

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§10.73(i).

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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.

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

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

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Quantum Inverse Scattering Method and Correlation Functions. Cambridge University Press, Cambridge.

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ISBN 0-521-37320-4; 0-521-58646-1, MathReview (Makoto Idzumi), ZentralBlatt

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§26.20.

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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

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MathReview (S. Chandrasekhar), ZentralBlatt

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§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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ISSN 0001-5962, Document, MathReview Entry, ZentralBlatt

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§22.19(iv).

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18: Bibliography F

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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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MathReview (R. F. Millar)

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§9.16.

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Semiclassical description of scattering. Ann. Physics 7 (3), pp. 259–286.

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ISSN 0003-4916, Document, MathReview, ZentralBlatt

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§9.16.

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Application of semiclassical scattering analysis. Ann. Physics 7 (3), pp. 287–322.

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ISSN 0003-4916, Document, MathReview, ZentralBlatt

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§9.16.

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19: Bibliography V

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An integral transform involving Heun functions and a related eigenvalue problem. SIAM J. Math. Anal. 17 (3), pp. 688–703.

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ISSN 0036-1410, Document, MathReview (William L. Perry), ZentralBlatt

Referenced by:

§31.10(i).

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Light Scattering by Small Particles. John Wiley and Sons. Inc., New York.

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MathReview (P. M. Morse)

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§9.16.

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Multiple Light Scattering. Vol. 1, Academic Press, New York.

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§6.17.

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20: Bibliography O

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Error bounds for asymptotic expansions in turning-point problems. J. Soc. Indust. Appl. Math. 12 (1), pp. 200–214.

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Document, MathReview (N. D. Kazarinoff), ZentralBlatt

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§2.8(iii).

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Numerical solution of Riemann-Hilbert problems: Painlevé II. Found. Comput. Math. 11 (2), pp. 153–179.

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ISSN 1615-3375, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§32.17, §32.17.

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Scattering by a parabolic cylinder—a uniform asymptotic expansion. J. Math. Phys. 26 (4), pp. 854–860.

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ISSN 0022-2488, Document, MathReview (Jean-Louis Guiraud)

Referenced by:

§12.17.

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