Free vs. Observed Quantum Evolution

FIGURE 4.6 The chart of Heisenberg Uncertainty Relationship (HUR) appearance for observed and free quantum evolutions covering the complete scale of the particle to wave ratios as computed from the Eqs. (4.556) and (4.562), respectively the points Q and a correspond to wave-particle precise equivalence and to the special extended-HURs of Eqs. (4.563) and (4.564), respectively (Putz, 2010c). 

Note that the possibility a quantum object is manifested only under particle behavior i.e., for PAV qo) is forbidden this is an important consequence of the present analytical discourse that is in agreement with the Copenhagen interpretation according which the quantum phenomena are merely manifested as undulatory (viz. Schrodinger equation) although some particle information may be contained but never in an exclusive manner (naturally, otherwise the Newtonian object would exist with no Planck constant and HUR relevance upon it). 

However, the wave-particle duality matches perfectly and always with HUR in its standard (Schrodinger) formulation of Eq. (2.99) on the other side, the wave-particle exact equivalence (PAV = 1) may be acquired only in the free evolution regime that, in turn, it is driven by modified HUR as given by Eq. (4.563). In other words, it seems that any experiment or observation upon a quantum object or system would destroy the PAV balance specific for free quantum evolution towards the undulatory manifestation through measurement. 

having the analytical expressions for both observed and free quantum evolutions may considerably refine our imderstanding of macro- and micro-universe. For instance, with various (PAV) 

It is worth giving a woiking example for emphasizing the reliability of the present approach and to choose for this aim the fundamental Compton 

---