  Schr\"odinger 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
Schr\"odinger 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.
