  It is shown how the Schrodinger equation can be transformed to a complex
quantum Navier-Stokes equation with imaginary dilatational viscosity. The
self-diffusion in quantum gases is described by this complex quantum
hydrodynamics and the quantum Marangoni effect is introduced. The density
matrix operator and Wigner function equations, corresponding to quantum
hydrodynamics, are described. Finally, the quantum teleportation in time is
also discussed via a non-relativistic version of the Majorana equation.
