INEQUIVALENCE BETWEEN THE SCHRODINGER-EQUATION AND THE MADELUNG HYDRODYNAMIC EQUATIONS

By differentiating the Schrodinger equation and separating the real an d imaginary parts, one obtains the Madelung hydrodynamic equations, wh ich have inspired numerous classical interpretations of quantum mechan ics. Such interpretations frequently assume that these equations are e quivalent to the Schrodinger equation, and thus provide an alternative basis for quantum mechanics. This paper proves that this is incorrect : to recover the Schrodinger equation, one must add by hand a quantiza tion condition, as in the old quantum theory. The implications for var ious alternative interpretations of quantum mechanics are discussed.