Detailed behavior of the phase‐integral approximations at zeros and singularities of the square of the base function

Autor:	Andrzej A. Skorupski
Rok vydání:	1988
Předmět:	Simple (abstract algebra) Mathematical analysis Phase (waves) Order (group theory) Statistical and Nonlinear Physics Gravitational singularity Wave equation Mathematical Physics Square (algebra) WKB approximation Mathematics Power (physics)
Zdroj:	Journal of Mathematical Physics. 29:1814-1823
ISSN:	1089-7658 0022-2488
Popis:	Approximate solutions to the one‐dimensional time independent wave equation, called the phase‐integral approximations, are analyzed in the vicinity of characteristic points. The approximations are of arbitrary order and are generated from an unspecified base function. The general theory is illustrated by examples involving the power and/or the exponential behavior of the square of the base function. In these cases simple estimates are derived for the integrals which define the accuracy of the phase‐integral approximation, and the optimum approximation order is determined.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::3d889212daab78199449df61027b7a64 https://doi.org/10.1063/1.527883 Zobrazit plný text záznamu