Instability and quantization in quantum hydrodynamics

Yakir Aharonov, Tomer Shushi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We show how the quantum hydrodynamical formulation of quantum mechanics converts the nonlocality in the standard wave-like description of quantum systems by an instability of the quantum system, which opens the door to a new way for studying quantum systems based on known methodologies for studying the stability of fluids. As a second result, we show how the Madelung equations describe quantized energies without any external quantization conditions.

Original languageEnglish
Article number2450268
JournalModern Physics Letters B
StateAccepted/In press - 2024


  • Current density
  • energy levels
  • Madelung equations
  • nonlocality
  • phase difference
  • quantization
  • quantum hydrodynamics


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