Exact solution of the Schrodinger equation across an arbitrary one‐dimensional piecewise‐linear potential barrier
作者:
Wayne W. Lui,
Masao Fukuma,
期刊:
Journal of Applied Physics
(AIP Available online 1986)
卷期:
Volume 60,
issue 5
页码: 1555-1559
ISSN:0021-8979
年代: 1986
DOI:10.1063/1.337788
出版商: AIP
数据来源: AIP
摘要:
A simple yet exact method of solving the Schrodinger equation across an arbitrary one‐dimensional piecewise‐linear potential is described. It is based on the analytical solution of the Schrodinger equation across a linear potential, where the solution can be expressed as a linear combination of the Airy functions. Proper boundary conditions are imposed at the interface between adjacent linear intervals of the potential, and a transfer‐matrix procedure is utilized in the derivation. The quantum mechanical transmission coefficient across a potential barrier and eigenenergies of a potential well can also be easily calculated using this method.
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