  The Wigner distribution function is a quasi-probability distribution. When
properly integrated, it provides the correct charge and current densities, but
it gives negative probabilities in some points and regions of the phase space.
Alternatively, the Husimi distribution function is positive-defined everywhere,
but it does not provide the correct charge and current densities. The origin of
all these difficulties is the attempt to construct a phase space within a
quantum theory that does not allow well-defined (i.e. simultaneous) values of
the position and momentum of an electron. In contrast, within the (de
Broglie-Bohm) Bohmian theory of quantum mechanics, an electron has well-defined
position and momentum. Therefore, such theory provides a natural definition of
the phase space probability distribution and by construction, it is
positive-defined and it exactly reproduces the charge and current densities.
The Bohmian distribution function has many potentialities for quantum problems,
in general, and for quantum transport, in particular, that remains unexplored.
