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31: Bruce R. Miller

… ►There, he carried out research in non-linear dynamics and celestial mechanics, developing a specialized computer algebra system for high-order Lie transformations. …

32: 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). …

33: 1.1 Special Notation

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$x,y$	real variables.
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$\mathrm{deg}$	degree.
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►In the physics, applied maths, and engineering literature a common alternative to $\overline{a}$ is $a^{\ast }$, $a$ being a complex number or a matrix; the Hermitian conjugate of $𝐀$ is usually being denoted ${𝐀}^{†}$.

34: 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). ►

Solvable Models of Statistical Mechanics

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35: Bibliography M

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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.

Encodings:

BibTeX

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Bessel Functions for Engineers. 2nd edition, Clarendon Press, Oxford.

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Notes:

The first edition was published in 1934 by Clarendon Press. The second edition was published originally in 1955.

External Links:

ZentralBlatt

Referenced by:

§10.73(iii).

Encodings:

BibTeX

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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).

Encodings:

BibTeX

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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).

Encodings:

BibTeX

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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).

Encodings:

BibTeX

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36: Gloria Wiersma

… ►Then she began working with the staff of the Physics Laboratory Office of Electronic Commerce in Scientific and Engineering Data, developing and refining the Laboratory website until her retirement in 2007. …

37: 18.38 Mathematical Applications

… ►The monic Chebyshev polynomial $2^{1-n}{T}_n\left(x\right)$, $n\ge 1$, enjoys the ‘minimax’ property on the interval $[-1,1]$, that is, $|2^{1-n}{T}_n\left(x\right)|$ has the least maximum value among all monic polynomials of degree $n$. … ►If the nodes in a quadrature formula with a positive weight function are chosen to be the zeros of the $n$th degree OP with the same weight function, and the interval of orthogonality is the same as the integration range, then the weights in the quadrature formula can be chosen in such a way that the formula is exact for all polynomials of degree not exceeding $2n-1$. … ►

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. …

38: Bibliography P

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Algorithm 385: Exponential integral $\mathrm{Ei}(x)$ . Comm. ACM 13 (7), pp. 446–447.

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Notes:

Includes Fortran code, maximum accuracy 20D. For certification and remarks see same journal v. 13 (1970), pp. 448–449 and p. 750; v. 15 (1972), p. 1074.

External Links:

ISSN 0001-0782, Document

Referenced by:

§6.21(ii).

Encodings:

BibTeX

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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).

Encodings:

BibTeX

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39: 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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Hunter and Kuriyan (1976) and Rushchitsky and Rushchitska (2000) for wave mechanics.

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Fukui and Horiguchi (1992) for quantum theory.

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40: 12.17 Physical Applications

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