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1: 14.31 Other Applications

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§14.31(ii) Conical Functions

… ►These functions are also used in the Mehler–Fock integral transform (§14.20(vi)) for problems in potential and heat theory, and in elementary particle physics (Sneddon (1972, Chapter 7) and Braaksma and Meulenbeld (1967)). …

2: 19.18 Derivatives and Differential Equations

… ►The next four differential equations apply to the complete case of $R_F$ and $R_G$ in the form $R_{-a}(\frac{1}{2},\frac{1}{2};z_1,z_2)$ (see (19.16.20) and (19.16.23)). … ►Similarly, the function $u=R_{-a}(\frac{1}{2},\frac{1}{2};x+\mathrm{i}y,x-\mathrm{i}y)$ satisfies an equation of axially symmetric potential theory: …

3: 19.33 Triaxial Ellipsoids

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§19.33(ii) Potential of a Charged Conducting Ellipsoid

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4: Bibliography S

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Resonances in $n$-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory. Ann. of Math. (2) 97, pp. 247–274.

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External Links:

ISSN 0003-486X, Document, Link, MathReview (K. Kumar)

Referenced by:

§1.18(viii).

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Mixed Boundary Value Problems in Potential Theory. North-Holland Publishing Co., Amsterdam.

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External Links:

MathReview (R. Shail), ZentralBlatt

Referenced by:

§10.22(iv).

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Hypergeometric and Legendre Functions with Applications to Integral Equations of Potential Theory. National Bureau of Standards Applied Mathematics Series, No. 19, U. S. Government Printing Office, Washington, D.C..

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MathReview, ZentralBlatt

Referenced by:

§13.23(iv), Ch.14, §31.3(iii).

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5: 15.18 Physical Applications

… ►More varied applications include photon scattering from atoms (Gavrila (1967)), energy distributions of particles in plasmas (Mace and Hellberg (1995)), conformal field theory of critical phenomena (Burkhardt and Xue (1991)), quantum chromo-dynamics (Atkinson and Johnson (1988)), and general parametrization of the effective potentials of interaction between atoms in diatomic molecules (Herrick and O’Connor (1998)).

6: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►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 $r\in [0,\mathrm{\infty })$. …

7: Bibliography B

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The attractive Coulomb potential polynomials. Constr. Approx. 1 (2), pp. 103–119.

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ISSN 0176-4276, Document, Link, MathReview (W. A. Al-Salam)

Referenced by:

§18.39(iv), §18.39(iv).

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Random and Restricted Walks: Theory and Applications. Gordon and Breach, New York.

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ZentralBlatt

Referenced by:

§16.24(i).

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Uniform approximation for potential scattering involving a rainbow. Proc. Phys. Soc. 89 (3), pp. 479–490.

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Document, ZentralBlatt

Referenced by:

§36.14(iii), §9.16.

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A class of solvable potentials. Nuovo Cimento (10) 25, pp. 864–879.

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Document, MathReview (S. Rosendorff), ZentralBlatt

Referenced by:

§15.18.

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Stability of repulsive Bose-Einstein condensates in a periodic potential. Phys. Rev. E (3) 63 (036612), pp. 1–11.

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Document

Referenced by:

§29.19(i).

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8: 23.21 Physical Applications

§23.21 Physical Applications

… ►In §22.19(ii) it is noted that Jacobian elliptic functions provide a natural basis of solutions for problems in Newtonian classical dynamics with quartic potentials in canonical form $(1-x^2)(1-k^2{x}^2)$. The Weierstrass function $\mathrm{\wp }$ plays a similar role for cubic potentials in canonical form $g_3+g_{2}x-4x^3$. … ►

Quantum field theory. See Witten (1987).

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String theory. See Green et al. (1988a, §8.2) and Polchinski (1998, §7.2).

9: Bibliography D

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Multiplicative Number Theory. 3rd edition, Graduate Texts in Mathematics, Vol. 74, Springer-Verlag, New York.

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Notes:

Revised and with a preface by Hugh L. Montgomery

External Links:

ISBN 0-387-95097-4, MathReview, ZentralBlatt

Referenced by:

§27.12.

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Pólya’s Theory of Counting. In Applied Combinatorial Mathematics, E. F. Beckenbach (Ed.), pp. 144–184.

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External Links:

ISBN 0898741726

Referenced by:

§26.20.

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Wave function for smooth potential and mass step. Phys. Rev. A 59 (1), pp. 107–112.

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Document

Referenced by:

§15.18.

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Elements of the Theory of Numbers. Harcourt/Academic Press, San Diego, CA.

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External Links:

ISBN 0-12-209130-2, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

Ch.24.

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Supersymmetry, shape invariance, and exactly solvable potentials. Amer. J. Phys. 56, pp. 163–168.

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Referenced by:

§18.38(iii).

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10: 29.19 Physical Applications

… ►Bronski et al. (2001) uses Lamé functions in the theory of Bose–Einstein condensates. … ►Ward (1987) computes finite-gap potentials associated with the periodic Korteweg–de Vries equation. …