ABSTRACT
The Schrodinger equation is solved for a quantum wire under the influence of a confinement potential in two directions. The wave function and energy levels for electrons are determined. The equation for the current flowing in the wire is derived in terms of the transmission coefficient for electrons across the contact/quantum wire interface, showing the dependence of electron concentration and temperature. At very low temperatures, the conductance contains two factors: a constant term, the quantum of conductance and a summation term over transmission coefficients. The Landauer formula thus obtained is also derived by considering the current carried with a single energy level in a conductor at zero temperature and progressing to one with multiple energy levels at non-zero temperature. In the light of the Landauer formula, the deviations from Ohm’s law and the relevant length scales for their occurrence are discussed. The generalization of the Landauer formula to the Büttiker formula is described.
