Is Dark Matter Quantum Coherent in Astrophysical Scales?

There exists a considerable evidence that astrophysical objects obey quantization rules with a gigantic value of Planck constant. Nottale and Da Rocha explain the findings in terms of fractal hydrodynamics modellable in terms of Schrödinger equation with an effective Planck constant whose general form is fixed by Equivalence Principle. In this article an interpretation as a genuine quantum effect based on quantization of Planck constant allowing dark matter to be quantum coherent in astrophysical scales is discussed. The model predicts correctly the value of the velocity parameter appearing in the gravitational Planck constant and explains the appearance of its harmonics and sub-harmonics. A quantum model for the formation of planetary system is proposed. Some numerical coincidences support the view that quantum coherent dark matter could be also responsible for the properties of living matter.