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Solving the one‐dimensional quantum mechanics problems using the matter wave multireflection

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1 Author(s)
Polak, Wieslaw ; Department of Physics, Technical University of Lublin, ul. Nadbystrzycka 38, 20‐618 Lublin, Poland

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This article presents a simple, yet general and exact analytic‐numerical method of solving one‐dimensional quantum mechanics problems. It is based on the concept of dividing an arbitrary potential into convenient segments and analyzing the multiple reflection of a plane matter wave between neighboring potential walls. Amplitude reflection and transmission coefficients of each segment are the basis for the analysis. A simple iterative technique for calculating them by a square barrier approximation is given. This method is applicable to various potential barriers, wells, and periodic structures including continuous variations of potential energy and particle effective mass.

Published in:

Journal of Applied Physics  (Volume:74 ,  Issue: 2 )