dorsal/arxiv
View SchemaOn the transfer matrix method and WKB approximation for Schr\"{o}dinger equation with position-dependent effective mass
| Authors | C. F. Huang, S. D. Chao, D. R. Hang, Y. C. Lee |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506153 |
| URL | https://arxiv.org/abs/quant-ph/0506153 |
| Journal | Chinese J. Phys. 46, 231 (2008) |
Abstract
We have obtained a set of coupled differential equations from the continuous limit of the transfer matrix method. Decoupling such a set of equations yields an extension to the Wentzel-Kramers-Brillouin (WKB) approximation for the Schr\"{o}dinger equation with the position-dependent effective mass (PDEM). In the classically allowed region, the decoupling is to ignore the reflection resulting from the variations of both the potential and effective mass. By considering an infinite-well example with the PDEM, it is shown that the extended WKB approximation can provide not only an estimation to eigenenergies, but also an analytic form to approximate wavefunctions.
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"abstract": "We have obtained a set of coupled differential equations from the continuous\nlimit of the transfer matrix method. Decoupling such a set of equations yields\nan extension to the Wentzel-Kramers-Brillouin (WKB) approximation for the\nSchr\\\"{o}dinger equation with the position-dependent effective mass (PDEM). In\nthe classically allowed region, the decoupling is to ignore the reflection\nresulting from the variations of both the potential and effective mass. By\nconsidering an infinite-well example with the PDEM, it is shown that the\nextended WKB approximation can provide not only an estimation to eigenenergies,\nbut also an analytic form to approximate wavefunctions.",
"arxiv_id": "quant-ph/0506153",
"authors": [
"C. F. Huang",
"S. D. Chao",
"D. R. Hang",
"Y. C. Lee"
],
"categories": [
"quant-ph",
"cond-mat.mtrl-sci"
],
"journal_ref": "Chinese J. Phys. 46, 231 (2008)",
"title": "On the transfer matrix method and WKB approximation for Schr\\\"{o}dinger equation with position-dependent effective mass",
"url": "https://arxiv.org/abs/quant-ph/0506153"
},
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