Improvement on the WKB method using an algebraic formalism

1979 ◽  
Vol 12 (8) ◽  
pp. 1155-1164 ◽  
Author(s):  
E G Sauter
Keyword(s):  
Wkb Method ◽  
Algebraic Formalism

Valence states of atoms and their conversions

1984 ◽  
Vol 49 (5) ◽  
pp. 1247-1261 ◽  
Author(s):  
Jaroslav Koča ◽  
Milan Kratochvíl ◽  
Milan Kunz ◽  
Vladimír Kvasnička
Keyword(s):  
Chemical Reactions ◽  
Computer Assisted ◽  
Efficient Tool ◽  
Common Features ◽  
Systematic Application ◽  
Organic Syntheses ◽  
Valence States ◽  
Algebraic Formalism

The algebraic formalism for the description of valence states of atoms and their interconversions is elaborated. It offers a possibility to construct and trace mechanistic paths of chemical reactions, the problem of which is of great importance in computer-assisted organic syntheses. Its systematic application gives exhaustive lists of possible mechanistic paths, and furthermore, very efficient tool to classify chemical reactions and look for their common features.

Wave action on currents with vorticity

1999 ◽  
Vol 386 ◽  
pp. 329-344 ◽  
Author(s):  
BENJAMIN S. WHITE
Keyword(s):  
Phase Shift ◽  
Deep Water ◽  
Current Velocity ◽  
Wave Action ◽  
Ray Theory ◽  
Wkb Method ◽  
Interaction Of Waves ◽  
New Equation ◽  
Spatially Varying

The interaction of waves on deep water with spatially varying currents may be described by a ray theory, with the wave amplitudes determined by the principle of conservation of wave action (CWA). However, all previous deep water derivations of CWA are restricted to the case of an irrotational current. In this paper, both the ray theory and CWA are derived by a WKB method without the assumption of irrotationality. Also derived is a new equation for a spatially varying phase shift which is not predicted by the usual ray theory, and which, in general, displaces the positions of the wave crests by a distance on the order of a wavelength. This phase shift, which is caused by variations of the current velocity with depth, vanishes in the irrotational case, and so is in accord with the irrotational theory.

C*‐algebraic formalism for coarse graining. I. General theory

1974 ◽  
Vol 15 (8) ◽  
pp. 1343-1347 ◽  
Author(s):  
John C. Wolfe ◽  
Gérard G. Emch
Keyword(s):  
General Theory ◽  
Coarse Graining ◽  
Algebraic Formalism

scholarly journals The Multiple Scattering of Electrons and Positrons

1954 ◽  
Vol 7 (2) ◽  
pp. 217 ◽  
Author(s):  
CBO Mohr ◽  
LJ Tassie
Keyword(s):  
Angular Distribution ◽  
Multiple Scattering ◽  
Born Approximation ◽  
Single Scattering ◽  
Mean Square ◽  
Wkb Method ◽  
Electrons And Positrons

The angular distribution of the single scattering of 33, 121, and 1065 keV electrons at small angles in gold is calculated and compared with the distributions given by the Born approximation and by the WKB method as used by Moli�re. The single scattering distribution for 1065 keV electrons is integrated numerically to give mean square angles of multiple scattering, and these are compared with the values given by the various multiple scattering theories.

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