quantum mechanics

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11: Michael V. Berry

… ►Berry has published numerous papers on theoretical physics, mainly in quantum mechanics and optics and including the development of associated mathematics, especially asymptotics and geometry. …

12: 12.17 Physical Applications

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

13: 31.17 Physical Applications

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§31.17(ii) Other Applications

►Heun functions appear in the theory of black holes (Kerr (1963), Teukolsky (1972), Chandrasekhar (1984), Suzuki et al. (1998), Kalnins et al. (2000)), lattice systems in statistical mechanics (Joyce (1973, 1994)), dislocation theory (Lay and Slavyanov (1999)), and solution of the Schrödinger equation of quantum mechanics (Bay et al. (1997), Tolstikhin and Matsuzawa (2001), and Hall et al. (2010)). … ►More applications—including those of generalized spheroidal wave functions and confluent Heun functions in mathematical physics, astrophysics, and the two-center problem in molecular quantum mechanics—can be found in Leaver (1986) and Slavyanov and Lay (2000, Chapter 4). …

14: 28.33 Physical Applications

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Meixner and Schäfke (1954, §§4.1, 4.2, and 4.7) for quantum mechanical problems and rotation of molecules.

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Fukui and Horiguchi (1992) for quantum theory.

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15: 5.20 Physical Applications

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Rutherford Scattering

►In nonrelativistic quantum mechanics, collisions between two charged particles are described with the aid of the Coulomb phase shift $\mathrm{ph}\mathrm{\Gamma }\left(\mathrm{\ell }+1+\mathrm{i}\eta \right)$; see (33.2.10) and Clark (1979). …

16: 18.39 Applications in the Physical Sciences

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§18.39(i) Quantum Mechanics

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18.39.6Moved to (errata.6).

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Referenced by:

§18.39(i)

Permalink:

http://dlmf.nist.gov/18.39.E6

See also:

Annotations for §18.39(i), §18.39 and Ch.18

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Introduction and One-Dimensional (1D) Systems

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1D Quantum Systems with Analytically Known Stationary States

… ►c) A Rational SUSY Potential argument …

17: Bibliography S

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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).

Encodings:

BibTeX

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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.

Encodings:

BibTeX

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General relativity and quantum mechanics: towards a generalization of the Lambert $W$ function: a generalization of the Lambert $W$ function. Appl. Algebra Engrg. Comm. Comput. 17 (1), pp. 41–47.

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External Links:

ISSN 0938-1279, Document, FullText, MathReview (E. Capelas de Oliveira), ZentralBlatt

Referenced by:

§4.13, §4.13.

Encodings:

BibTeX

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The Gaussian Function in Calculations of Statistical Mechanics and Quantum Mechanics. In Methods in Computational Physics: Advances in Research and Applications, B. Alder, S. Fernbach, and M. Rotenberg (Eds.), Vol. 2, pp. 1–45.

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Referenced by:

§8.24(i), §8.24(iii).

Encodings:

BibTeX

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Spectral Methods in Chemistry and Physics. Applications to Kinetic Theory and Quantum Mechanics. Scientific Computation, Springer-Verlag, Dordrecht.

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External Links:

ISBN 978-94-017-9453-4; 978-94-017-9454-1, Document, Link, MathReview (Gabriel Stoltz)

Referenced by:

§18.38(i), §18.39(iii), §18.39(iii), §18.39(iii).

Encodings:

BibTeX

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18: 18.38 Mathematical Applications

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Supersymmetric Quantum Mechanics (SUSY)

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EOP’s, Painlevé Transcendents, and Quantum Mechanics

►EOP’s are the subject of recent work on rational solutions to the fourth Painlevé equation, see Clarkson (2003a) and Marquette and Quesne (2016),where use of Hermite EOP’s makes a connection to quantum mechanics. …

19: Bibliography W

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Lectures on Quantum Mechanics. Cambridge University Press, Cambridge, UK.

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External Links:

ISBN 978-1-107-02872-2

Referenced by:

§18.39(ii).

Encodings:

BibTeX

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Group Theory and its Application to the Quantum Mechanics of Atomic Spectra. Pure and Applied Physics. Vol. 5, Academic Press, New York.

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Notes:

Expanded and improved ed. Translated from the German by J. J. Griffin.

External Links:

ISBN 0-12-750550-4, MathReview (A. S. Wightman), ZentralBlatt

Referenced by:

§34.12.

Encodings:

BibTeX

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20: Bibliography E

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Angular Momentum in Quantum Mechanics. 3rd printing, with corrections, 2nd edition, Princeton University Press, Princeton, NJ.

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Notes:

Reprinted in 1996.

External Links:

ISBN 0-691-02589-4, MathReview, ZentralBlatt

Referenced by:

§14.30(i), §14.30(ii), §14.30(iii), §14.30(iv), §14.30(iv), §14.31(iii), (34.1.1), §34.1, §34.1, §34.13, §34.2, §34.3(i), §34.3(i), §34.3(ii), §34.3(iii), §34.3(iv), §34.3(vii), §34.3(vii), §34.4, §34.5(i), §34.5(ii), §34.5(iii), §34.5(iv), §34.5(vi), §34.6, §34.7(i), §34.7(ii), §34.7(iv), §34.7(vi), Ch.34, Erratum (V1.0.14) for Section 34.1, Erratum (V1.0.15) for Section 34.1.

Encodings:

BibTeX

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