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| Main Author: | |
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| Format: | Preprint |
| Published: |
2016
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1611.00247 |
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Table of Contents:
- I provide a transfer matrix method for the Foldy-Wouthuysen representation of the Dirac equation. I derive the relationship between the reflection and transmission coefficients of the Dirac spinors and the wavefunction in the transformed representation. I develop a WKB approximation for Dirac fermions that has the same elegant form as the WKB solution to Schrödinger's equation. My WKB approximation is to all orders and includes the semi-classical turning point. I provide an extension to fully 2-dimensional periodic structures by Fourier methods for band-gap engineering. I verify my methods for all energies by comparison with analytic solutions developed in the Dirac spinor representation. Rich appendices detail my research into the Green's functions of Dirac fermions, where I rigorously derive the free space Green's functions for the Foldy-Wouthuysen representation of the Dirac equation.