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1: 8.24 Physical Applications

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§8.24(i) Incomplete Gamma Functions

►The function $\gamma (a,x)$ appears in: discussions of power-law relaxation times in complex physical systems (Sornette (1998)); logarithmic oscillations in relaxation times for proteins (Metzler et al. (1999)); Gaussian orbitals and exponential (Slater) orbitals in quantum chemistry (Shavitt (1963), Shavitt and Karplus (1965)); population biology and ecological systems (Camacho et al. (2002)). … ►

§8.24(iii) Generalized Exponential Integral

… ►With more general values of $p$, $E_p\left(x\right)$ supplies fundamental auxiliary functions that are used in the computation of molecular electronic integrals in quantum chemistry (Harris (2002), Shavitt (1963)), and also wave acoustics of overlapping sound beams (Ding (2000)).

2: 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).

Encodings:

BibTeX

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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).

Encodings:

BibTeX

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3: Bibliography R

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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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External Links:

Document

Referenced by:

§34.13.

Encodings:

BibTeX

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4: 18.39 Applications in the Physical Sciences

… ►Derivations of (18.39.42) appear in Bethe and Salpeter (1957, pp. 12–20), and Pauling and Wilson (1985, Chapter V and Appendix VII), where the derivations are based on (18.39.36), and is also the notation of Piela (2014, §4.7), typifying the common use of the associated Coulomb–Laguerre polynomials in theoretical quantum chemistry. … ►

Table 18.39.1: Typical Non-Classical Weight Functions Of Use In DVR Applications^a

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Name of OP System	$w(x)$	$[a,b]$	Notation	Applications
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Half-Rys	$\exp \left(-\alpha x^2\right)$	$[0,1]$	$R_n(x,\alpha )$	Quantum Chemistry Quadraturesi,j
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5: Bibliography S

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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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6: William P. Reinhardt

… … ► 1942 in San Francisco, California) is Professor of Chemistry and Adjunct Professor of Physics at the University of Washington, Seattle, currently Emeritus. …He is both an Associate Editor for Chemistry and a Senior Associate Editor for the DLMF. Reinhardt is a frequent visitor to the NIST Physics Laboratory in Gaithersburg, and to the Joint Quantum Institute (JQI) and Institute for Physical Sciences and Technology (ISTP) at the University of Maryland. …