Electronic structure of the two-dimensional gas in the uniform perpendicular magnetic field and uniform transverse electric field

In this study, the electronic structure of two-dimensional electron gas was examined. For this purpose, the definition of two-dimensional electron gas with the Hamiltonian of the system after the statement was derived. Initially the Hamiltonian expression via vector potential and Landau gauge transformations were described. Then the system of free particle states, the confining potential and the electric field cases were examined in the presence and in these three cases the energy eigenvalues and eigenfunctions of the system was calculated analytically. Then the definition of Green's functions in three cases to be used in the solution of the Hamiltonian Green's functions expression was obtained. Using the finite element method the system of energy was calculated and the energy graphics were plotted. The resulting solutions and graphics were compared with articles in the literature, and the results were found compatible. The energy produced in the presence of electric field in comparison with other studies the edges of graphic sharp outputs rather than was found to be soft outputs. After studies found to be consistent of the system both the confining potential and in the presence of electric field cases were investigated and express the Hamiltonian of the system was derived analytically. Green's function to be used in the solution of the Hamiltonian expression was obtained analytically. Finally The Hamiltonian of the system by making the dimensionless expression finite element method was used and was obtained energy graphic of the system. Unlike other studies energy of graphic values higher than an electric field produced.