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1: 24.18 Physical Applications

§24.18 Physical Applications

►Bernoulli polynomials appear in statistical physics (Ordóñez and Driebe (1996)), in discussions of Casimir forces (Li et al. (1991)), and in a study of quark-gluon plasma (Meisinger et al. (2002)). …

2: 15.18 Physical Applications

… ►The hypergeometric function has allowed the development of “solvable” models for one-dimensional quantum scattering through and over barriers (Eckart (1930), Bhattacharjie and Sudarshan (1962)), and generalized to include position-dependent effective masses (Dekar et al. (1999)). ►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)).

3: 7.21 Physical Applications

§7.21 Physical Applications

… ►Fried and Conte (1961) mentions the role of $w\left(z\right)$ in the theory of linearized waves or oscillations in a hot plasma; $w\left(z\right)$ is called the plasma dispersion function or Faddeeva (or Faddeyeva) function; see Faddeeva and Terent’ev (1954). … ►These applications include astrophysics, plasma diagnostics, neutron diffraction, laser spectroscopy, and surface scattering. …

4: 9.16 Physical Applications

… ►The KdV equation and solitons have applications in many branches of physics, including plasma physics lattice dynamics, and quantum mechanics. …

5: Bibliography M

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A dispersion function for plasmas containing superthermal particles. Physics of Plasmas 2 (6), pp. 2098–2109.

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§15.18.

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Phenomenological equations of state for the quark-gluon plasma. Phys. Rev. D 65 (3), pp. (034009–1)–(034009–10).

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§24.18.

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6: Bibliography F

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The Plasma Dispersion Function: The Hilbert Transform of the Gaussian. Academic Press, London-New York.

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Notes:

Erratum: Math. Comp. v. 26 (1972), no. 119, p. 814.

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§7.21.

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7: 18.39 Applications in the Physical Sciences

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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-Freud Druvesteyn	$\exp \left(-x^4\right)$	$[0,\mathrm{\infty })$	$D_n(x)$	Electron Transport in Plasmasd
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8: Bibliography C

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Nonclassical Symmetry Reductions and Exact Solutions for Physically Significant Nonlinear Evolution Equations. In Nonlinear and Chaotic Phenomena in Plasmas, Solids and Fluids (Edmonton, AB, 1990), W. Rozmus and J. A. Tuszynski (Eds.), pp. 72–79.

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§29.19(ii).

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