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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.
Published in:
Journal of Applied Physics
(Volume:60
,
Issue:
5
)
Date of Publication: Sep 1986
- Page(s):
- 1555 - 1559
- ISSN :
- 0021-8979
- Digital Object Identifier :
- 10.1063/1.337788
- Product Type:
- Journals & Magazines
- Date of Current Version :
- 07 July 2009
- Issue Date :
- Sep 1986
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