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

J. Walker
J. Gathright
Journal / Anthology

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

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.

*Science > Physics > Quantum Physics

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