quantum scattering

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11: 12.17 Physical Applications

… ►Dean (1966) describes the role of PCFs in quantum mechanical systems closely related to the one-dimensional harmonic oscillator. …

12: 18.39 Applications in the Physical Sciences

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The Quantum Coulomb Problem: Scattering States

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13: 10.73 Physical Applications

… ►Bessel functions enter in the study of the scattering of light and other electromagnetic radiation, not only from cylindrical surfaces but also in the statistical analysis involved in scattering from rough surfaces. … … ►

§10.73(ii) Spherical Bessel Functions

… ►Accordingly, the spherical Bessel functions appear in all problems in three dimensions with spherical symmetry involving the scattering of electromagnetic radiation. …In quantum mechanics the spherical Bessel functions arise in the solution of the Schrödinger wave equation for a particle in a central potential. …

14: William P. Reinhardt

… ►Reinhardt is a frequent visitor to the NIST Physics Laboratory in Gaithersburg, and to the Joint Quantum Institute (JQI) and Institute for Physical Sciences and Technology (ISTP) at the University of Maryland. … ►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. …

15: Bibliography G

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

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§15.18.

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Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials. J. Phys. A 47 (1), pp. 015203, 26 pp..

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ISSN 1751-8113, Document, Link, MathReview (Brian Simanek)

Referenced by:

§18.36(vi), §18.36(vi).

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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)

Referenced by:

§9.11(iv), §9.17(iii).

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Quantum mechanics: fundamentals. Second edition, Springer-Verlag, New York.

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ISBN 0-387-22023-2, MathReview (Howard E. Brandt), ZentralBlatt

Referenced by:

§18.39(i).

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Quantum Electrodynamics of Strong Fields: With an Introduction into Modern Relativistic Quantum Mechanics. Texts and Monographs in Physics, Springer.

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Referenced by:

§33.22(iv).

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16: Bibliography M

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Crossing symmetric expansions of physical scattering amplitudes: The $O(2,1)$ group and Lamé functions. J. Mathematical Phys. 12, pp. 281–293.

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Document, MathReview

Referenced by:

§29.19(ii).

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Connection between quantum systems involving the fourth Painlevé transcendent and $k$-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial. J. Math. Phys. 57 (5), pp. Paper 052101, 15 pp..

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ISSN 0022-2488, Document, Link, MathReview Entry

Referenced by:

§18.38(iii).

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Geometrical and Catastrophe Optics Methods in Scattering. In Physical Acoustics, A. D. Pierce and R. N. Thurston (Eds.), Vol. 21, pp. 1–234.

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§36.14(ii).

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Complex-energy method for elastic $e$-H scattering above the ionization threshold. Phys. Rev. Lett. 23 (7), pp. 361–363.

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1st item.

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Quantum Mechanics. Vol. I. North-Holland Publishing Co., Amsterdam.

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Notes:

Translated from the French by G. M. Temmer

External Links:

MathReview (A. S. Wightman), ZentralBlatt

Referenced by:

§10.73(ii).

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17: Bibliography S

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Quantum Chaos, Symmetry and Zeta Functions. Lecture I, Quantum Chaos. In Current Developments in Mathematics, 1997 (Cambridge, MA), R. Bott (Ed.), pp. 127–144.

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MathReview (Shin-ya Koyama), ZentralBlatt

Referenced by:

§25.17.

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Use of analyticity in the calculation of nonrelativistic scattering amplitudes. Phys. Rev. 167, pp. 1411–1423.

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Document, Link

Referenced by:

(18.40.9), §18.40(ii).

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Exact recursive evaluation of $3j$- and $6j$-coefficients for quantum-mechanical coupling of angular momenta. J. Mathematical Phys. 16 (10), pp. 1961–1970.

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Document, MathReview (J.-L. Calais)

Referenced by:

§34.13, §34.3(iii).

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Variational calculations of scattering. Ann. Phys. 16, pp. 36–50.

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§18.39(iv).

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Quantum defect theory. Rep. Prog. Phys. 46 (2), pp. 167–257.

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§33.14(i), §33.22(ii).

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18: Bibliography F

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Discrete Painlevé equations and their appearance in quantum gravity. Comm. Math. Phys. 142 (2), pp. 313–344.

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ISSN 0010-3616, Link, MathReview (Nikolai A. Kostov), ZentralBlatt

Referenced by:

§32.15.

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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

Referenced by:

§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 B

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Electromagnetic Scattering and its Applications. Applied Science Publishers, London.

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External Links:

ISBN 0-85334-955-X

Referenced by:

§10.73(i), §10.73(ii).

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The Scattering of Electromagnetic Waves from Rough Surfaces. Pergamon Press, New York.

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Notes:

Reprinted in 1987 by Artech House Publishers, Norwood, Massachusetts.

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ISBN 0-89006-238-2, ZentralBlatt

Referenced by:

§10.73(i).

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Uniform approximation for potential scattering involving a rainbow. Proc. Phys. Soc. 89 (3), pp. 479–490.

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Document, ZentralBlatt

Referenced by:

§36.14(iii), §9.16.

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Cusped rainbows and incoherence effects in the rippling-mirror model for particle scattering from surfaces. J. Phys. A 8 (4), pp. 566–584.

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Document, MathReview

Referenced by:

§36.14(iii).

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The asymptotic analysis of canonical problems in high-frequency scattering theory. II. The circular and parabolic cylinders. Proc. Cambridge Philos. Soc. 74, pp. 313–332.

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Document, MathReview (Y. M. Chen)

Referenced by:

§12.17.

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20: Bibliography C

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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

Referenced by:

§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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Referenced by:

§14.31(iii).

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Supersymmetry and quantum mechanics. Phys. Rep. 251, pp. 267–385.

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Referenced by:

§18.38(iii).

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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

Referenced by:

§18.39(v).

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Schrödinger Operators, with Applications to Quantum Mechanics and Global Geometry. Springer Verlag, New York.

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External Links:

ISBN 978-3-540-16758-7

Referenced by:

§1.18(vii), §1.18(x).

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