Numerical solution of the Schröbinger equation for an electron in a potential well of an arbitrary form

A numerical model is proposed for the solution of the Schröbinger equation. The model is based on the scattering matrix of the solution region. The scattering matrix is formed from matrices of partial regions of a simple shape. The density of the self-emission current for a metal/vacuum potential ba...

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Bibliographic Details
Published in:Journal of communications technology & electronics 2014-08, Vol.59 (8), p.843-846
Main Authors: Komarov, D. A., Morev, S. P., Darmaev, A. N., Ryadnov, A. Yu
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Boundary conditions
Communications Engineering
Communications equipment
Density
Electric fields
Electron transfer
Electronics
Engineering
Error analysis
Integral equations
Mathematical analysis
Mathematical models
Networks
Optoelectronics
Potential barriers
Scattering
Schrodinger equation
Software packages
Studies
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Summary:A numerical model is proposed for the solution of the Schröbinger equation. The model is based on the scattering matrix of the solution region. The scattering matrix is formed from matrices of partial regions of a simple shape. The density of the self-emission current for a metal/vacuum potential barrier of an arbitrary form is calculated. The results of test calculation of electron transmission through a rectangular potential barrier with a relative error less than 0.001% as compared to the analytical solution are presented.
ISSN:1064-2269
1555-6557
DOI:10.1134/S1064226914080117