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Electron-Wave-Function Calculation in the Continuous Part of the Spectrum: The Case of Slowly Varying Potential Asymptotics

M. Tadic
Z. Ikonic
V. Milanovic
Journal / Anthology

Physical Review E
Year: 1996
Volume: 53
Issue: 6
Page range: 6523-6529

In this paper we address the problem of calculating the free-state wave functions with predefined asymptotic behavior. It is shown that, in a number of cases, usable results may be obtained by the WBK (Wentzel-Brillouin-Kramers) approximation, but not by plain numerical integration of the Schrodinger equation if it is performed with accuracy normally provided by computers. For reference purposes, the calculation based on algebra implemented in Mathematica is done, enabling an arbitrary large number of significant digits to be used. The WBK-based calculation is found to offer reasonably low errors.

*Applied Mathematics > Numerical Methods
*Science > Physics > Quantum Physics