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WBK Approximation for Continuum States with Predefined Asymptotics
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| Publications of the Faculty of Electrical Engineering, University of Belgrade |
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In this paper we address the problem of calculating the free state wave functions with predefined asymptotic behaviour (two-point boundary value problem). It is shown that, in a number of cases, usable results may be obtained by WBK approximation, but not only by plain numerical integration of the Schrödinger equation if it is performed with accuracy normally provided by computers (for reference purposes, the almost exact calculation was done by a Mathematica program, enabling an arbitrary large number of significant digits to be used). The WBK based calculation is found to offer reasonably low errors. A heuristic explanation of the validity of the total depletion approximation in the self-consistent calculations of semiconductor quantum well is given.
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