Abstract
In this paper, we try to present a way in terms of which one cananalytically obtain the Hartree self-consistent potential instead ofcomputing it by the numerical iterative procedure as usual, which isconvenient for us to describe the current flow through a mesoscopicconductor. In our treatment, we expand the action function S(x) by Planckconstant ℏ, then the self-consistent potential and the wavefunctioncan be solved analytically order by order starting from the Poisson equationand quantum Hamilton–Jacobian equation, the differential conductance andquantum capacitance can thus be obtained naturally. In our paper, we showthe quantum corrections up to the second order, and the electron-electroninteraction is considered only at the Hartree approximation level.
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