Schrodinger equation with given, a priori known current is formulated. A nonzero 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 nonlinear self-consistent Schrodinger 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.