Madelung equations

Summary

The Madelung equations rewrite the Schrödinger equation as the equations of a compressible fluid. The squared modulus of the wave function becomes a density, and the gradient of its phase becomes a velocity. The result is a continuity equation and an Euler-type momentum equation with an extra force from the quantum potential. They are the basis of quantum hydrodynamics and of the fluid description of superfluids.