  The extension of the Ramo-Schockley-Pellegrini theorem for quantum systems
allows to define a positive-operator valued measure (POVM) for the total
conduction plus displacement electrical current. The resulting current operator
is characterized by two parameters, viz. the width of the associated Gaussian
functions and the lapse of time between consecutive measurements. For large
Gaussian dispersions and small time intervals, the operator obeys to a
continuous weak-measurement scheme. Contrarily, in the limit of very narrow
Gaussian widths and a single-shot measurement, the operator corresponds to a
standard von Neumann (projective) measurement. We have implemented the
resulting measurement protocol into a quantum electron transport simulator.
Numerical results for a resonant tunneling diode show the great sensibility of
current-voltage characteristics to different parameter configurations of the
total current operator.
