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11: Bibliography

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The Riemann Hypothesis and the Hamiltonian of a Quantum Mechanical System. In Number Theory and Dynamical Systems (York, 1987), M. M. Dodson and J. A. G. Vickers (Eds.), London Math. Soc. Lecture Note Ser., Vol. 134, pp. 153–172.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§25.17.

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Normal forms of functions near degenerate critical points, the Weyl groups $A_k,D_k,E_k$ and Lagrangian singularities. Funkcional. Anal. i Priložen. 6 (4), pp. 3–25 (Russian).

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Notes:

In Russian. English translation: Functional Anal. Appl., 6(1973), pp. 254–272.

External Links:

MathReview (G. R. Belickii), ZentralBlatt

Referenced by:

§36.2(i).

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Special Functions: Group Theoretical Aspects and Applications. D. Reidel Publishing Co., Dordrecht.

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Notes:

Reprinted by Kluwer Academic Publishers, Boston, 2001.

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ISBN 90-277-1822-9; 1-4020-0319-6, MathReview, ZentralBlatt

Referenced by:

Profile Richard A. Askey, Profile Tom H. Koornwinder.

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12: Bibliography C

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Work Group of Computational Mathematics, University of Kassel, Germany.

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Computer Algebra and Orthogonal Polynomials: a Web service using Maple for online generation of formulas and graphs of orthogonal polynomials belonging to the Askey scheme. For further information see Swarttouw (1997) and Koepf (1999).

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CAOP

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1st item.

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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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Quasinormal modes of the extremal BTZ black hole. Classical Quantum Gravity 21 (12), pp. 2801–2809.

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ISSN 0264-9381, MathReview (Donato Bini), ZentralBlatt

Referenced by:

§13.28(iii).

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Handbook of Continued Fractions for Special Functions. Kluwer Academic Publishers Group, Dordrecht.

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Referenced by:

Profile Annie A. M. Cuyt.

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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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13: Bibliography R

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Research Institute for Symbolic Computation, Hagenberg im Mühlkreis, Austria.

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Notes:

Software packages for hypergeometric and $q$-hypergeometric summation, sequences and power series, permutation groups, partition analysis, and difference equations.

External Links:

RISC Combinatorics Group

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6th item.

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Calculation of $3n$-$j$ symbols by Labarthe’s method. International Journal of Quantum Chemistry 63 (1), pp. 57–64.

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Document

Referenced by:

§34.13.

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14: 18.38 Mathematical Applications

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Group Representations

►For group-theoretic interpretations of OP’s see Vilenkin and Klimyk (1991, 1992, 1993). … ►The Dunkl operator, introduced by Dunkl (1989), is an operator associated with reflection groups or root systems which has terms involving first order partial derivatives and reflection terms. … ►

Supersymmetric Quantum Mechanics (SUSY)

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EOP’s, Painlevé Transcendents, and Quantum Mechanics

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15: Bibliography N

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Numerical Algorithms Group, Ltd..

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Notes:

The NAG Libraries are large general purpose numerical software libraries with broad coverage of elementary and special functions. Implementations are in single and double precision.

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§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

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Confluent hypergeometric equations and related solvable potentials in quantum mechanics. J. Math. Phys. 41 (12), pp. 7964–7996.

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ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§13.28(i).

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Affine Weyl groups, discrete dynamical systems and Painlevé equations. Comm. Math. Phys. 199 (2), pp. 281–295.

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ISSN 0010-3616, Document, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt

Referenced by:

§32.2(v).

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16: Bibliography S

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The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions. 2nd edition, Graduate Texts in Mathematics, Vol. 203, Springer-Verlag, New York.

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Notes:

First edition published by Wadsworth & Brooks/Cole Advanced Books & Software, 1991.

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ISBN 0-387-95067-2, MathReview, ZentralBlatt

Referenced by:

§26.19.

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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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External Links:

MathReview (Shin-ya Koyama), ZentralBlatt

Referenced by:

§25.17.

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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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External Links:

Document, MathReview (J.-L. Calais)

Referenced by:

§34.13, §34.3(iii).

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Semiclassical approximations to $3j$- and $6j$-coefficients for quantum-mechanical coupling of angular momenta. J. Mathematical Phys. 16 (10), pp. 1971–1988.

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External Links:

Document, MathReview (J.-L. Calais)

Referenced by:

§34.8.

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

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Document

Referenced by:

§33.14(i), §33.22(ii).

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