Trace identities for the Schröedinger operator and the WKB method

1982 ◽  
pp. 178-183 ◽  
Author(s):  
G. Parisi
Keyword(s):  
Wkb Method ◽  
Schroedinger Operator

SEMIFACTORIZATION OF THE MULTIDIMENSIONAL SCHROEDINGER OPERATOR

1989 ◽  
Vol 50 (C3) ◽  
pp. C3-87-C3-88
Author(s):  
A. CSIZMAZIA
Keyword(s):  
Schroedinger Operator

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.

scholarly journals Application of the WKB method to catenary-shaped slender structures

2008 ◽  
Vol 48 (1-2) ◽  
pp. 249-257 ◽  
Author(s):  
Ioannis K. Chatjigeorgiou
Keyword(s):  
Wkb Method ◽  
Slender Structures

The WKB method and differential consequences of the Riccati equation

2011 ◽  
Vol 89 (5-6) ◽  
pp. 885-892
Author(s):  
N. L. Chuprikov
Keyword(s):  
Riccati Equation ◽  
Wkb Method
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