Is the quantum hydrodynamic analogy more general than the Schroedinger approach?

Abstract: The quantum hydrodynamic analogy (QHA), equivalent to the Schr\"odinger equation, is investigated and extended to the stochastic case. The investigation shows that in addition to reproducing the standard quantum mechanics the QHA model is able to generally describe the quantum stochastic dynamics leading to the dissipative Schr\"odinger equation given by Kostin [55] as a particular case. The inspection shows that the QHA is well suited for the treatment of problems where local noise (spatially distributed one) is introduced. In this case the analysis shows that the bi-univocal correspondence between the QHA and the Schr\"odinger approach breaks down and that the states described by the QHA do not have their corresponding ones into the Schr\"odinger description.