On the transfer matrix method and WKB approximation for Schrödinger equation with position-dependent effective mass

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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 Schrödinger 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.
10 pages, 3 figures, and 1 table. The revised manuscript has been accepted by Chinese Journal of Physics

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Quantum Physics, Materials Science

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http://salesiana.dossiersoluciones.com/handle/123456789/163632

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/quant-ph/0506153
 http://arxiv.org/abs/quant-ph/0506153
 Chinese J. Phys. 46, 231 (2008)

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arXiv