integrable systems

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11: Vadim B. Kuznetsov

… ►Kuznetsov published papers on special functions and orthogonal polynomials, the quantum scattering method, integrable discrete many-body systems, separation of variables, Bäcklund transformation techniques, and integrability in classical and quantum mechanics. …

12: 36.14 Other Physical Applications

… ►Diffraction catastrophes describe the “semiclassical” connections between classical orbits and quantum wavefunctions, for integrable (non-chaotic) systems. …

13: Bibliography H

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Numerical Tools for the Study of Finite Gap Solutions of Integrable Systems. Ph.D. Thesis, Technischen Universität Berlin.

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Notes:

(All relevant material, plus corrections, are included in Deconinck et al. (2004).)

External Links:

ZentralBlatt

Referenced by:

§21.5(i).

Encodings:

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14: Bibliography

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Spinning Tops: A Course on Integrable Systems. Cambridge Studies in Advanced Mathematics, Vol. 51, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-56129-9; 0-521-77919-7, MathReview (Emma Previato), ZentralBlatt

Referenced by:

§22.19(iv).

Encodings:

BibTeX

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15: Bibliography B

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Integrable Hamiltonian systems and the Painlevé property. Phys. Rev. A (3) 25 (3), pp. 1257–1264.

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External Links:

ISSN 0556-2791, Document, MathReview

Referenced by:

§32.16.

Encodings:

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16: 18.39 Applications in the Physical Sciences

… ►The finite system of functions ${\psi }_n$ is orthonormal in $L^2(ℝ,dx)$, see (18.34.7_3). …

17: Bibliography T

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High Speed Numerical Integration of Fermi Dirac Integrals. Master’s Thesis, Naval Postgraduate School, Monterey, CA.

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External Links:

FullText

Referenced by:

§25.21(vii).

Encodings:

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Angular Momentum: An Illustrated Guide to Rotational Symmetries for Physical Systems. A Wiley-Interscience Publication, John Wiley & Sons Inc., New York.

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Notes:

With 1 Macintosh floppy disk (3.5 inch; DD). Programs for the calculation of $3j,6j,9j$ symbols are included.

External Links:

ISBN 0-471-55264-X, MathReview (J. F. Cornwell), ZentralBlatt

Referenced by:

§34.3(vii).

Encodings:

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18: Bibliography C

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Toward symbolic integration of elliptic integrals. J. Symbolic Comput. 28 (6), pp. 739–753.

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Notes:

Code written by J. FitzSimons to generate reduction tables for elliptic integrals symbolically in the Derive computer algebra system is available.

External Links:

ISSN 0747-7171, Document, Code, MathReview (Axel Riese), ZentralBlatt

Referenced by:

§19.29(i), §19.29(ii), §19.29(ii), §19.29(ii), §19.29(ii).

Encodings:

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19: 23.21 Physical Applications

… ►Airault et al. (1977) applies the function $\mathrm{\wp }$ to an integrable classical many-body problem, and relates the solutions to nonlinear partial differential equations. … ►

§23.21(iii) Ellipsoidal Coordinates

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20: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

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§1.18(ii) $L^2$ spaces on intervals in $ℝ$

… ►For a Lebesgue–Stieltjes measure $d\alpha$ on $X$ let $L^2(X,d\alpha )$ be the space of all Lebesgue–Stieltjes measurable complex-valued functions on $X$ which are square integrable with respect to $d\alpha$, … ►We integrate by parts twice giving: … ►Eigenfunctions corresponding to the continuous spectrum are non-$L^2$ functions. … ►Similar results hold for two, but not higher, dimensional quantum systems. …