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

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

2005-06-18

arxiv.org/abs/quant-ph/0506153v2

Chinese J. Phys. 46, 231 (2008)

Physics

Quantum Physics

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

Scientific paper

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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