Correction for the Uniform WKB Wave Functions and the WKB Phase Shifts

1974 ◽  
Vol 52 (18) ◽  
pp. 1805-1815 ◽  
Author(s):  
Byung Chan Eu ◽  
Hervé G. Guerin
Keyword(s):  
Numerical Solution ◽  
Present Method ◽  
Turning Point ◽  
Numerical Test ◽  
Equation Of Motion ◽  
Phase Shifts ◽  
Wave Functions ◽  
Wkb Approximation ◽  
Wkb Method ◽  
Connection Formulas

A method of improving the uniform WKB solution for single turning point problems is discussed and the correction formulas for the WKB phase shifts are obtained. The method involves the equation of motion which is in a form similar to that used by Fröman and Fröman to obtain the connection formulas in the WKB approximation. A sequence of solutions to the equation of motion is obtained in a remarkably compact form—and in a novel way—by utilizing the involutionality of certain 2 × 2 matrices appearing in the equations. A numerical test of the result thus obtained is presented in comparison with the corresponding numerical solution result. Unlike the ordinary WKB method, the present method is completely free of the connection formulas of the WKB approximation.

The numerical solution for problems of turning point without resonance

1985 ◽  
Vol 6 (5) ◽  
pp. 439-446 ◽  
Author(s):  
Lin Peng-cheng ◽  
Yan Peng-xiang
Keyword(s):  
Numerical Solution ◽  
Turning Point

scholarly journals Numerical solution of an integral equation arising in the problem of cruciform crack using Daubechies scale function

2019 ◽  
Vol 14 (1) ◽  
pp. 21-27
Author(s):  
Jyotirmoy Mouley ◽  
M. M. Panja ◽  
B. N. Mandal
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Numerical Solution ◽  
Present Method ◽  
Numerical Results ◽  
Scale Function ◽  
Forcing Term ◽  
Classical Integral

Abstract This paper is concerned with obtaining approximate numerical solution of a classical integral equation of some special type arising in the problem of cruciform crack. This integral equation has been solved earlier by various methods in the literature. Here, approximation in terms of Daubechies scale function is employed. The numerical results for stress intensity factor obtained by this method for a specific forcing term are compared to those obtained by various methods available in the literature, and the present method appears to be quite accurate.

scholarly journals Klein Gordon Field in FLRW Space-Time

2020 ◽  
Vol 13 (13) ◽  
pp. 1-4
Author(s):  
S.K. Sharma ◽  
P.R. Dhungel ◽  
U. Khanal
Keyword(s):  
Spherical Harmonics ◽  
Energy Momentum Tensor ◽  
Equation Of Motion ◽  
Momentum Tensor ◽  
Space Time ◽  
Wkb Approximation ◽  
Temporal Parts ◽  
Klein Gordon ◽  
Current Energy ◽  
Particle Current

As a continuation of solving the equations governing the perturbation of the Friedmann-Lemaitre-Robertson- Walker (FLRW) space-time in Newman-Penrose formalism, the behaviour of the massive Klein-Gordon (KG) field coupled to the FLRW has been investigated. The Equation of Motion has been written and solved separately for radial and temporal parts. The former solution has come to be in terms of the Gegenbauer polynomials and spherical harmonics and the latter being in the WKB approximation. The particle current, energy momentum tensor and potential have also been obtained.

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