Schroedinger equation for current carrying states
arXiv:cond-mat/0209347 · doi:10.1063/1.1460857
Abstract
Schrödinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization of the total energy on the manifold of an arbitrary current density topology results into a non-linear self-consistent Schrödinger equation. The applications to electronic transport in two-terminal molecular devices are developed and new macroscopic definition of a molecular current-voltage characteristic is proposed. The Landauer formula for the conductance of an ideal one-dimensional lead is obtained within the approach. The method is examined by modeling of current carrying states of one-dimensional harmonic oscillator.
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