On the Transfer Matrix Method and the WKB Approximation for the Schrödinger Equation with Position-Dependent Effective Mass

C. F. Huang；S. D. Chao；D. R. Hang；Y. C. Lee

Chinese Journal of Physics

46卷3期（2008 / 06 / 01）

231 - 241

英文

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 a 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 a PDEM, it is shown that the extended WKB approximation can provide not only an estimation of the eigenenergies, but also an analytic form for the approximate wavefunctions.

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