for spherically symmetric systems

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1: 18.39 Applications in the Physical Sciences

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§18.39(ii) A 3D Separable Quantum System, the Hydrogen Atom

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2: Bibliography S

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The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions. 2nd edition, Graduate Texts in Mathematics, Vol. 203, Springer-Verlag, New York.

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Notes:

First edition published by Wadsworth & Brooks/Cole Advanced Books & Software, 1991.

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ISBN 0-387-95067-2, MathReview, ZentralBlatt

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§26.19.

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Rational surfaces associated with affine root systems and geometry of the Painlevé equations. Comm. Math. Phys. 220 (1), pp. 165–229.

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ISSN 0010-3616, Document, MathReview (I. Dolgachev), ZentralBlatt

Referenced by:

§32.7(viii).

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Decoherent dynamics of a two-level system coupled to a sea of spins. Phys. Rev. Lett. 81 (26), pp. 5710–5713.

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Document

Referenced by:

§11.12.

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Text-book on Spherical Astronomy. Fifth edition, Cambridge University Press, Cambridge.

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MathReview

Referenced by:

§4.42(iii).

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Some combinatorial properties of Jack symmetric functions. Adv. Math. 77 (1), pp. 76–115.

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ISSN 0001-8708, Document, MathReview (Dennis White), ZentralBlatt

Referenced by:

§18.37(iii).

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3: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

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Self-Adjoint and Symmetric Operators

… ►Similar results hold for two, but not higher, dimensional quantum systems. … ►which appear in the quantum theory of binding or scattering of a particle in a spherically symmetric potential $V(r)$ in three dimensions, and where $r\in [0,\mathrm{\infty })$. … ►A linear operator $T$ with dense domain is called symmetric if … ►

Self-adjoint extensions of a symmetric Operator

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4: Bibliography C

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Reduction theorems for elliptic integrands with the square root of two quadratic factors. J. Comput. Appl. Math. 118 (1-2), pp. 71–85.

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Code written by the second author to compute symmetric elliptic integrals numerically in the Derive computer algebra system is available.

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ISSN 0377-0427, Document, Code, MathReview, ZentralBlatt

Referenced by:

§19.29(ii), §19.36(i), §19.36(i), §19.39(iv).

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Asymptotic approximations for symmetric elliptic integrals. SIAM J. Math. Anal. 25 (2), pp. 288–303.

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ISSN 0036-1410, Document, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§19.12, §19.27(ii), §19.27(iii), §19.27(iv), §19.27(v), §19.27(vi).

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On the expansion of a Coulomb potential in spherical harmonics. Proc. Cambridge Philos. Soc. 46, pp. 626–633.

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Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§34.12.

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Inequalities for a symmetric elliptic integral. Proc. Amer. Math. Soc. 25 (3), pp. 698–703.

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FullText, MathReview (Y. L. Luke), ZentralBlatt

Referenced by:

§19.24(ii), §19.9(ii).

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Extremal measures for a system of orthogonal polynomials. Constr. Approx. 9, pp. 111–119.

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ISSN 0176-4276, Document, MathReview (Mizan Rahman), ZentralBlatt

Referenced by:

§18.28(iv).

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5: Bibliography M

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Some conjectures for root systems. SIAM J. Math. Anal. 13 (6), pp. 988–1007.

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ISSN 0036-1410, Document, MathReview (S. Milne), ZentralBlatt

Referenced by:

§17.13, §17.14.

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Symmetric Functions and Orthogonal Polynomials. University Lecture Series, Vol. 12, American Mathematical Society, Providence, RI.

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ISBN 0-8218-0770-6, MathReview (Angèle M. Hamel), ZentralBlatt

Referenced by:

§17.14.

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Orthogonal polynomials associated with root systems. Sém. Lothar. Combin. 45, pp. Art. B45a, 40 pp. (electronic).

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ISSN 1286-4889, FullText, MathReview, ZentralBlatt

Referenced by:

§18.37(iii).

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System for the manipulation of symbolic and numerical expressions. Includes a collection of special functions. Utilizes exact fractions, arbitrary precision integers, and arbitrary precision floating point numbers.

External Links:

Home Page

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

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SciFace Software, Paderborn, Germany.

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Computer algebra system for doing symbolic and exact algebraic computations as well as numerical calculations with almost arbitrary accuracy

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§ ‣ Software Cross Index.

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6: Bibliography D

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Complex zeros of linear combinations of spherical Bessel functions and their derivatives. SIAM J. Math. Anal. 4 (1), pp. 128–133.

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ISSN 1095-7154, Document, MathReview (C. J. Bouwkamp), ZentralBlatt

Referenced by:

§10.58.

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The principal frequencies of vibrating systems with elliptic boundaries. Quart. J. Mech. Appl. Math. 8 (3), pp. 361–372.

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Document, MathReview (M. A. Hyman), ZentralBlatt

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3rd item.

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Chebyshev series for the spherical Bessel function $j_l(r)$ . Comput. Phys. Comm. 18 (1), pp. 73–86.

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Document

Referenced by:

§10.76(iii).

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Texas Instruments, Inc..

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Notes:

Symbolic and extended-precision numerical computing system.

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index.

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An Introduction to Chaotic Dynamical Systems. The Benjamin/Cummings Publishing Co. Inc., Menlo Park, CA.

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ISBN 0-8053-1601-9, MathReview (Richard C. Churchill), ZentralBlatt

Referenced by:

§3.8(viii).

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