Formal Heisenberg Indeterminacy

A directly application and of an extreme importance of the de Broglie wave packet is to consider its normalization by noting that the wave function in the real space and the amplitude in the reciprocal space (or of the impetus by the de Broglie quantification) are conjugate size in the sense of the Fourier mutual transforms. 

Remarkably, the coupling is of the order of Planck constant - which once again justifies the previous statement, that this constant is universal, is immutable necessary in characterization of the movement, both in the observable space (of the coordinate) or of diffraction (of the momentum). 

Note that the last relationship is called the Heisenberg type , because it only justifies and does not demonstrates - it actually expressing that the impulse and the coordinate are inseparable at the level of Planck constant and can not be distinctly seen at spatiotemporal level, while being driven by it. 

Although currently (as a matter of fact even since its publication by Heisenberg in 1927) are heated discussions and attempts to dismantle the dogma imposed by limiting/Heisenberg uncertainty in the Planck constant, the utility of this relationship (even borderline) is incontestable, which will be illustrated also by application to the Hydrogen atom (Bohr model), immediately below, and latter in a more elaborate framework. 

Considering the hydrogen atom as the model (simple) of the circular motion of the electron around the nucleus, the coordinate variation (on circular direction) and momentum (on radial direction) recorded by the electron are expressed such as 

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