electronic structure of heavy elements

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21: Bibliography B

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The Calculation of Spherical Bessel Functions and Coulomb Functions. In Computational Atomic Physics: Electron and Positron Collisions with Atoms and Ions, K. Bartschat and J. Hinze (Eds.), pp. 181–202.

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Notes:

Includes program disk. Double-precision Fortran code for positive energies. Maximum accuracy: 15D.

External Links:

ISBN 3-540-60179-1, FullText and Code

Referenced by:

3rd item, §33.8.

Encodings:

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Quantum mechanics of one- and two-electron atoms. Springer-Verlag, Berlin.

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External Links:

MathReview (L. Van Hove), ZentralBlatt

Referenced by:

§18.39(ii), §18.39(ii).

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Quantum Mechanics of One- and Two-electron Atoms. Rosetta edition, Plenum Publishing Corp., New York.

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Notes:

Reprint (with corrections) of the original edition published in 1957 by Springer and Academic Press

External Links:

MathReview, ZentralBlatt (D. Geissler)

Referenced by:

§1.18(viii), §33.22(ii), §33.22(ii), §33.22(v).

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One- and two-electron photoejection from ${\mathrm{H}}^{-}$: A multichannel $J$-matrix calculation. Phys. Rev. A 14, pp. 2159–2173.

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External Links:

Document, Link

Referenced by:

§18.39(iv).

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Elements of the Integral Calculus. 2nd edition, Ginn & Co., Boston.

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Notes:

Reprinted by G. E. Stechert, New York, 1926

Referenced by:

§19.11(i), Ch.19.

Encodings:

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22: 34.12 Physical Applications

§34.12 Physical Applications

… ►For applications in nuclear structure, see de-Shalit and Talmi (1963); in atomic spectroscopy, see Biedenharn and van Dam (1965, pp. 134–200), Judd (1998), Sobelman (1992, Chapter 4), Shore and Menzel (1968, pp. 268–303), and Wigner (1959); in molecular spectroscopy and chemical reactions, see Burshtein and Temkin (1994, Chapter 5), and Judd (1975). …

23: Bibliography I

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IEEE Standard for Floating-Point Arithmetic. The Institute of Electrical and Electronics Engineers, Inc..

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Notes:

IEEE Std 754-2008, Revision of IEEE Std 754-1985

External Links:

ISBN 978-0-7381-5753-5, Document

Referenced by:

§3.1(i).

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IEEE Standard for Interval Arithmetic: IEEE Std 1788-2015. The Institute of Electrical and Electronics Engineers, Inc..

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External Links:

ISBN 978-0-7381-9720-3, Document

Referenced by:

§3.1(ii), §3.1(ii), Erratum (V1.0.25) for Section 3.1.

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IEEE Standard for Interval Arithmetic: IEEE Std 1788.1-2017. The Institute of Electrical and Electronics Engineers, Inc..

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External Links:

ISBN 978-1-5044-4602-0, Document

Referenced by:

§3.1(ii), §3.1(ii), Erratum (V1.0.25) for Section 3.1.

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IEEE International Standard for Information Technology—Microprocessor Systems—Floating-Point arithmetic: IEEE Std 754-2019. The Institute of Electrical and Electronics Engineers, Inc..

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Notes:

IEEE Std ISO/IEC/IEEE 60559, Revision of IEEE Std 754-1985

External Links:

ISBN 978-2-88912-566-1, Document

Referenced by:

Figure 3.1.1, Figure 3.1.1, §3.1(i), §3.1(i), Erratum (V1.0.25) for Section 3.1.

Encodings:

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24: 22.18 Mathematical Applications

… ►With $k\in [0,1]$ the mapping $z\to w=\mathrm{sn}(z,k)$ gives a conformal map of the closed rectangle $[-K,K]\times [0,K^{\prime }]$ onto the half-plane $\mathrm{\Im }w\ge 0$, with $0,\pm K,\pm K+\mathrm{i}{K}^{\prime },\mathrm{i}{K}^{\prime }$ mapping to $0,\pm 1,\pm k^{-2},\mathrm{\infty }$ respectively. … ►This circumvents the cumbersome branch structure of the multivalued functions $x(y)$ or $y(x)$, and constitutes the process of uniformization; see Siegel (1988, Chapter II). … ►This provides an abelian group structure, and leads to important results in number theory, discussed in an elementary manner by Silverman and Tate (1992), and more fully by Koblitz (1993, Chapter 1, especially §1.7) and McKean and Moll (1999, Chapter 3). The existence of this group structure is connected to the Jacobian elliptic functions via the differential equation (22.13.1). …

25: 26.20 Physical Applications

… ►Applications of combinatorics, especially integer and plane partitions, to counting lattice structures and other problems of statistical mechanics, of which the Ising model is the principal example, can be found in Montroll (1964), Godsil et al. (1995), Baxter (1982), and Korepin et al. (1993). …

26: 26.22 Software

… ►For algorithms for counting and analyzing combinatorial structures see Knuth (1993), Nijenhuis and Wilf (1975), and Stanton and White (1986).

27: Alexander I. Bobenko

… ► Eitner), published by Springer in 2000, and Discrete Differential Geometry: Integrable Structure (with Y. …

28: 18.38 Mathematical Applications

… ►Schneider et al. (2016) discuss DVR/Finite Element solutions of the time-dependent Schrödinger equation. … ►It has elegant structures, including $N$-soliton solutions, Lax pairs, and Bäcklund transformations. … ►Algebraic structures were built of which special representations involve Dunkl type operators. In the $q$-case this algebraic structure is called the double affine Hecke algebra (DAHA), introduced by Cherednik. …This gives also new structures and results in the one-variable case, but the obtained nonsymmetric special functions can now usually be written as a linear combination of two known special functions. …

29: 21.7 Riemann Surfaces

… ►Removing the singularities of this curve gives rise to a two-dimensional connected manifold with a complex-analytic structure, that is, a Riemann surface. All compact Riemann surfaces can be obtained this way. ►Since a Riemann surface $\mathrm{\Gamma }$ is a two-dimensional manifold that is orientable (owing to its analytic structure), its only topological invariant is its genus $g$ (the number of handles in the surface). … ►Here $\sqrt{\zeta (P)}$ is such that ${\sqrt{\zeta (P)}}^2=\zeta (P)$, $P\in \mathrm{\Gamma }$. … ►Consider a fixed subset $U$ of $B$, such that the number of elements $|U|$ in the set $U$ is $g+1$, and $P_{\mathrm{\infty }}\notin U$. Next, define an isomorphism $𝜼$ which maps every subset $T$ of $B$ with an even number of elements to a $2g$-dimensional vector $𝜼(T)$ with elements either $0$ or $\frac{1}{2}$. …

30: 18.2 General Orthogonal Polynomials

… ►Assume $y\notin (a,b)$ in (18.2.12). … ►For OP’s $p_n(x)$ with weight function in the class $𝒢$ there are asymptotic formulas as $n\to \mathrm{\infty }$, respectively for $x\in ℂ$ outside $[-1,1]$ and for $x\in [-1,1]$, see Szegő (1975, Theorems 12.1.2, 12.1.4). … ►

Degree lowering and raising differentiation formulas and structure relations

… ►Then the OP’s are called semi-classical and (18.2.44) is called a structure relation. …