Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Foldy-Wouthuysen transfer matrix method for Dirac tunneling through
  monolayer graphene with a mass gap   We provide a transfer matrix method for the Foldy-Wouthuysen representation
of the Dirac equation. We develop the relationship between the reflection and
transmission coefficients of the Dirac spinors and the wavefunction in the
transformed representation. We develop a WKB approximation for Dirac fermions
which has the same elegant form as the WKB solution to Schr\"{o}dinger's
equation. Our WKB approximation is to all orders and includes the
semi-classical turning point. We provide an extension to fully 2-dimensional
periodic structures by Fourier methods for band engineering. We verify our
methods for all energies by comparison with analytic solutions developed in the
Dirac spinor representation. We also include a rich appendix detailing our
research into the Green's functions of Dirac fermions.

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The categories of this paper are: math
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The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
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The categories of this paper are: physics
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: math-ph