Usage of Schrödinger equation vs Madelung equations

Question

It is well known that Madelung formulation is alternative to the Schrödinger Formulation, cf. this previous Madelung transformation Phys.SE post. I wanted to know what makes Schrödinger's formulation superior to that of Madelung, and in particular, when does the Madelung formulation fail?

Answer 1

This is a translation from the German Wikipedia entry about the Madelung equations:

Due to their non-linearity, the Madelung-equations are difficult to use in practise. However, they show that there exist non-linear equations that are based on linear equations.

Hope this helps.