electric particle field

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21: 18.39 Applications in the Physical Sciences

… ►where $x$ is a spatial coordinate, $m$ the mass of the particle with potential energy $V(x)$, $\mathrm{\hslash }=h/(2\pi )$ is the reduced Planck’s constant, and $(a,b)$ a finite or infinite interval. ►Here the term $-\frac{{\mathrm{\hslash }}^2}{2m}\frac{{\partial }^2}{{\partial x}^2}$ represents the quantum kinetic energy of a single particle of mass $m$, and $V(x)$ its potential energy. As in classical dynamics this sum is the total energy of the one particle system. … ►allows anharmonic, or amplitude dependent, frequencies of oscillation about $x_e$, and also escape of the particle to $x=+\mathrm{\infty }$ with dissociation energy $D$. … ►For the potential $V(r)=+Z{e}^2/r$, corresponding to interaction of particles with like charges, there are no bound states, the continuum scattering states form a complete set for each $l$, as discussed in Chapter 33, and their discretized versions in §18.39(iv). …

22: Bibliography J

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Bounds on Dawson’s integral occurring in the analysis of a line distribution network for electric vehicles. Eurandom Preprint Series Technical Report 14, Eurandom, Eindhoven, The Netherlands.

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Notes:

ISSN 1389-2355

External Links:

FullText

Referenced by:

§7.8, §7.8.

Encodings:

BibTeX

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23: 27.19 Methods of Computation: Factorization

… ►These algorithms include the Continued Fraction Algorithm (cfrac), the Multiple Polynomial Quadratic Sieve (mpqs), the General Number Field Sieve (gnfs), and the Special Number Field Sieve (snfs). …

24: Peter Paule

… ►Paule’s main research interests are computer algebra and algorithmic mathematics, together with connections to combinatorics, special functions, number theory, and other related fields. …

25: Jim Pitman

… ►Pitman has devoted much effort to promote the development of open access resources in the fields of probability and statistics. …

26: 28.33 Physical Applications

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McLachlan (1947, Chapters XVI–XIX) for applications of the wave equation to vibrational systems, electrical and thermal diffusion, electromagnetic wave guides, elliptical cylinders in viscous fluids, and diffraction of sound and electromagnetic waves.

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27: 5.16 Sums

… ►For related sums involving finite field analogs of the gamma and beta functions (Gauss and Jacobi sums) see Andrews et al. (1999, Chapter 1) and Terras (1999, pp. 90, 149).

28: Mourad E. H. Ismail

… ► Rahman), Fields Institute Communications, v. …

29: Philip J. Davis

… ►Davis joined NBS in 1954 when it was becoming the leading center for an emerging field of mathematical research: numerical analysis. … ►At CalTech, John Todd dedicated himself to the training of new researchers in numerical analysis, and Olga Taussky, who had been a full-time NBS consultant influential in establishing the field of matrix theory, became the first woman at CalTech to attain the academic rank of full professor. ►Davis, easing into his role as Chief, did his part to promote the field of numerical analysis at NBS. …

30: 5.20 Physical Applications

… ►In nonrelativistic quantum mechanics, collisions between two charged particles are described with the aid of the Coulomb phase shift $\mathrm{ph}\mathrm{\Gamma }\left(\mathrm{\ell }+1+\mathrm{i}\eta \right)$; see (33.2.10) and Clark (1979). … ►

Elementary Particles

►Veneziano (1968) identifies relationships between particle scattering amplitudes described by the beta function, an important early development in string theory. …