<Dl> <Dd> Four - velocity U = γ (c, u →) = γ (c, v g n ^) (\ displaystyle \ mathbf (U) = \ gamma (c, (\ vec (\ mathbf (u)))) = \ gamma (c, v_ (g) (\ hat (\ mathbf (n))))) </Dd> </Dl> <Dd> Four - velocity U = γ (c, u →) = γ (c, v g n ^) (\ displaystyle \ mathbf (U) = \ gamma (c, (\ vec (\ mathbf (u)))) = \ gamma (c, v_ (g) (\ hat (\ mathbf (n))))) </Dd> <P> The physical reality underlying de Broglie waves is a subject of ongoing debate . Some theories treat either the particle or the wave aspect as its fundamental nature, seeking to explain the other as an emergent property . Some, such as the hidden variable theory, treat the wave and the particle as distinct entities . Yet others propose some intermediate entity that is neither quite wave nor quite particle but only appears as such when we measure one or the other property . The Copenhagen interpretation states that the nature of the underlying reality is unknowable and beyond the bounds of scientific inquiry . </P> <P> Schrödinger's quantum mechanical waves are conceptually different from ordinary physical waves such as water or sound . Ordinary physical waves are characterized by undulating real - number' displacements' of dimensioned physical variables at each point of ordinary physical space at each instant of time . Schrödinger's "waves" are characterized by the undulating value of a dimensionless complex number at each point of an abstract multi-dimensional space, for example of configuration space . </P>

Is there a way to quantify matter waves
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