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Title

A Transfer-Matrix Approach to One-Dimensional Quantum Mechanics Using Mathematica
Authors

J. Walker
J. Gathright
Journal / Anthology

Computers in Physics
Year: 1992
Volume: 6
Issue: 4
Page range: 393-399
Description

A variety of one-dimensional quantum systems is studied using a transfer-matrix formalism. In particular, only two matrices are required: one to propagate a wave function over a region of constant potential, the other to connect wave functions at a discontinuity in the potential. Using these simple matrices as building blocks, we constructed complex transfer matrices with which to study energy bands in one-dimensional crystals, as well as the intriguing characteristics of tranmission through multiple barriers. All systems studied here are modeled with finite-step potentials, not delta functions. The solutions obtained are exact and can be generated with relative ease using Mathematica. The method is throroughly explicated and several coding examples are provided.
Subject

*Science > Physics > Quantum Physics