Instability and quantization in quantum hydrodynamics

In this short paper, we show how a quantum nonlocal effect of far-apart wavepackets in the Schrodinger picture of wavefunctions is replaced by a local instability problem when considering the hydrodynamical formulation of quantum mechanics, known as the Madelung picture. As a second result, we show how the Madelung equations describe quantized energies without any external quantization conditions.