  Recently, it is shown that the extended phase space formulation of quantum
mechanics is a suitable technique for studying the quantum dissipative system.
Here, as an application of this formalism, we consider a dissipative system of
charged particles interacting with an external time dependent electric field.
Such a system has been investigating by Buch and Denman, and two solutions with
completely different structure have been obtained for Schr\"{o}dinger's
equation in two different gauges. We demonstrate how both gauges lead to the
same conductivity by generalizing the gauge transformations to the phase space
and using the extended phase space technique.
