  A nonlinear wave mechanical equation is proposed by inserting an imaginary
quantum potential into the Schr\"{o}dinger equation. An explicit expression for
its solution is given under certain assumptions and it is shown that it entails
attenuation related effects as non-unitary evolution, non-exponential quantum
decay and entropy production. In the quantum hydrodynamical formulation the
existence of circulation effects for the osmotic velocity field is established.
Finally, a time-invariant equation for the probability density is derived,
analogous to the tensor Lighthill equation in aeroacoustics, which admits both
retarded and advanced solutions.
