By differentiating the Schrödinger equation and separating the real amd imaginary parts, one obtains the Madelung hydrodynamic equations, which have inspired numerous classical interpretations of quantum mechanics. Such interpretations frequently assume that these equations are equivalent to the Schrödinger equation, and thus provide an alternative basis for quantum mechanics. This paper proves that this is incorrect: to recover the Schrödinger equation, one must add by hand a quantization condition, as in the old quantum theory. The implications for various alternative interpretations of quantum mechanics are discussed.

• Received 2 June 1993

DOI:https://doi.org/10.1103/PhysRevA.49.1613