Abstract. The present work is devoted to the computer modeling of emission processes from the graphene surface which is a promising material for modern applications. We examine the effect of the ion field inhomogeneity on the variational solution of the Schrödinger equation for the ground state of a loosely bound electron of a hydrogenlike carbon atom, which simulates the graphene model. This shows a significant impact of the allowance for the field inhomogeneity to the ground state of the electron.
This study is related to the development of mathematical methods and numerical algorithms for modeling the local quantum state of the graphene surface on the scale of the lattice spacing. Earlier, to solve this problem, a model of the graphene structure in the form of a lattice of hydrogen-like atoms with screened ions was proposed. However, the screening field was uniform. In this work, it is assumed that the screening field of the ion is inhomogeneous along the radius. The main direction of research was the calculation of the energy of the ground state of an electron in an inhomogeneous field.
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