q-deformed quantum mechanical

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31: 22.19 Physical Applications

… ►plays a prototypal role in classical mechanics (Lawden (1989, §5.2)), quantum mechanics (Schulman (1981, Chapter 29)), and quantum field theory (Pokorski (1987, p. 203), Parisi (1988, §14.6)). … ►Such solutions include standing or stationary waves, periodic cnoidal waves, and single and multi-solitons occurring in diverse physical situations such as water waves, optical pulses, quantum fluids, and electrical impulses (Hasegawa (1989), Carr et al. (2000), Kivshar and Luther-Davies (1998), and Boyd (1998, Appendix D2.2)). … ►Whittaker (1964, Chapter IV) enumerates the complete class of one-body classical mechanical problems that are solvable this way. …

32: Bibliography P

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Introduction to quantum mechanics. Dover Publications, Inc., New York.

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Notes:

With applications to chemistry, Reprint of the 1935 original

External Links:

ISBN 0-486-64871-0, MathReview Entry

Referenced by:

§1.18(v), §18.39(i), §18.39(ii), §18.39(ii).

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Ideas of Quantum Chemistry. second edition, Elsevier, Amsterdam-New York.

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External Links:

ISBN 978-0-444-59436-5

Referenced by:

§18.39(ii).

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33: Charles W. Clark

… … ► 1952 in Minneapolis, Minnesota) is a NIST Fellow (awarded in 2010) and a Fellow of the Joint Quantum Institute of NIST and the University of Maryland (awarded in 2007). … ►Clark’s current research interests are the dynamics of ultracold atoms and its application to quantum information, applications of synchrotron radiation, and the exploitation of atomic and molecular physics processes for new methods of neutron detection. … ►He has served as Chair of the Division of Atomic, Molecular, and Optical Physics of the APS, Chair of the Physics Section of the AAAS, and as Program Manager for Atomic, Molecular, and Quantum Physics at the U. …

34: Bibliography N

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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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External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§13.28(i).

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35: 34.10 Zeros

… ►In a $\mathit{3}j$ symbol, if the three angular momenta $j_1,j_2,j_3$ do not satisfy the triangle conditions (34.2.1), or if the projective quantum numbers do not satisfy (34.2.3), then the $\mathit{3}j$ symbol is zero. …However, the $\mathit{3}j$ and $\mathit{6}j$ symbols may vanish for certain combinations of the angular momenta and projective quantum numbers even when the triangle conditions are fulfilled. …

36: Tom H. Koornwinder

… ►Koornwinder has published numerous papers on special functions, harmonic analysis, Lie groups, quantum groups, computer algebra, and their interrelations, including an interpretation of Askey–Wilson polynomials on quantum SU(2), and a five-parameter extension (the Macdonald–Koornwinder polynomials) of Macdonald’s polynomials for root systems BC. …

37: 10.73 Physical Applications

… ►In quantum mechanics the spherical Bessel functions arise in the solution of the Schrödinger wave equation for a particle in a central potential. …

38: Bibliography D

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The constrained quantum mechanical harmonic oscillator. Proc. Cambridge Philos. Soc. 62, pp. 277–286.

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External Links:

Document, MathReview (T. Erber)

Referenced by:

§12.11(i), §12.11(i), §12.17.

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Quantum Fields and Strings: A Course for Mathematicians. Vol. 1, 2. American Mathematical Society, Providence, RI.

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Notes:

Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997

External Links:

ISBN 0-8218-1198-3, MathReview, ZentralBlatt

Referenced by:

§21.9.

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Hydrodynamic Stability. Cambridge University Press, Cambridge.

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Notes:

Cambridge Monographs on Mechanics and Applied Mathematics

External Links:

ISBN 0-521-22798-4, MathReview (Adelina Georgescu), ZentralBlatt

Referenced by:

(9.13.25), (9.13.27), (9.13.28), (9.13.29), (9.13.30), (9.13.35), (9.13.36), (9.13.37), Figure 9.13.1, Figure 9.13.1, Figure 9.13.2, Figure 9.13.2, §9.13(ii), §9.13(ii), §9.16.

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39: Bibliography H

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Quantum theory for mathematicians. Graduate Texts in Mathematics, Vol. 267, Springer, New York.

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External Links:

ISBN 978-1-4614-7115-8; 978-1-4614-7116-5, Document, Link, MathReview Entry

Referenced by:

§1.18(x).

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Analytic evaluation of two-center STO electron repulsion integrals via ellipsoidal expansion. Internat. J. Quantum Chem. 88 (6), pp. 701–734.

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External Links:

Document

Referenced by:

§8.24(iii).

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Asymptotic expansions of Mathieu functions in wave mechanics. J. Comput. Phys. 21 (3), pp. 319–325.

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External Links:

Document, MathReview (John P. Coleman)

Referenced by:

5th item.

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40: Bibliography M

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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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External Links:

ISSN 0022-2488, Document, Link, MathReview Entry

Referenced by:

§18.38(iii).

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Spin Systems, Statistical Mechanics and Painlevé Functions. In Painlevé Transcendents: Their Asymptotics and Physical Applications, D. Levi and P. Winternitz (Eds.), NATO Adv. Sci. Inst. Ser. B Phys., Vol. 278, pp. 377–391.

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Notes:

Proc. NATO Adv. Res. Workshop, Sainte-Adèle, Canada, 1990

External Links:

MathReview, ZentralBlatt

Referenced by:

§32.16.

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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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The Second Painlevé Transcendent: A Nonlinear Airy Function. In Mechanics Today, Vol. 5, pp. 297–313.

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External Links:

MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§32.11(ii), §32.17, §32.3(ii).

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Diatomic molecules according to the wave mechanics. II: Vibrational levels. Phys. Rev., II. Ser. 34, pp. 57–64.

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External Links:

ISSN 0031-899X, ZentralBlatt

Referenced by:

(18.39.16).

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