1. A mathematical basis for the graphene
- Author
-
Carlos Conca, Jorge San Martín, and Viviana Solano
- Subjects
Physics ,Differential equation ,Graphene ,Applied Mathematics ,Mathematical analysis ,law.invention ,Computational Mathematics ,symbols.namesake ,Honeycomb structure ,law ,Lattice (order) ,symbols ,Hamiltonian (quantum mechanics) ,Eigenvalues and eigenvectors - Abstract
We present a new basis of representation for the graphene honeycomb structure that facilitates the solution of the eigenvalue problem by reducing it to one dimension. We define spaces in these geometrical basis that allow us to solve the Hamiltonian in the edges of the lattice. We conclude that it is enough to analyze a one-dimensional problem in a set of coupled ordinary second-order differential equations to obtain the behavior of the solutions in the whole graphene structure.
- Published
- 2019
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