de Broglie Normal Modes in the Madelung Fluid

Eyal Heifetz*, Anirban Guha, Leo Maas

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


In an attempt to explore further the Madelung fluid-like representation of quantum mechanics, we derive the small perturbation equations of the fluid with respect to its basic states. The latter are obtained from the Madelung transform of the Schrödinger equation eigenstates. The fundamental eigenstates of de Broglie monochromatic matter waves are then shown to be mapped into the simple basic states of a fluid with constant density and velocity, where the latter is the de Broglie group velocity. The normal modes with respect to these basic states are derived and found to also satisfy the de Broglie dispersion relation. Despite being dispersive waves, their propagation mechanism is equivalent to that of sound waves in a classical ideal adiabatic gas. We discuss the physical interpretation of these results.

Original languageEnglish
Article number35
Number of pages12
JournalFoundations of Physics
Issue number2
Publication statusPublished - Apr 2023


  • De Broglie matter waves
  • Madelung fluid
  • Normal modes


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