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The quantum hydrodynamic analogy (QHA), equivalent to the Schr\"odingerequation, is investigated and extended to the stochastic case. Theinvestigation shows that in addition to reproducing the standard quantummechanics the QHA model is able to generally describe the quantum stochasticdynamics 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 thetreatment of problems where local noise (spatially distributed one) isintroduced. In this case the analysis shows that the bi-univocal correspondencebetween the QHA and the Schr\"odinger approach breaks down and that the statesdescribed by the QHA do not have their corresponding ones into theSchr\"odinger description.

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