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

Skorupski, Andrzej A.
August 1988
Journal of Mathematical Physics;Aug88, Vol. 29 Issue 8, p1814
Academic Journal
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.


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