A Many-Body Extension to Madelung Quantum Hydrodynamics*

In this talk we derive a many-body quantum-hydrodynamic model from first principles in the spirit of Madelung. We obtain exact time-dependent 3-D fluid equations that satisfy wave function symmetry or anti-symmetry, then obtain simplified forms for the cases of single permanent and Slater determinant with orthonormal basis functions. We show that, neglecting correlations and assuming many degenerate plane-wave electrons in the uniform limit, electron dynamics are governed by basic Euler equations with a mean-field Hartree interaction, Thomas–Fermi pressure, and Dirac exchange potential.