Remarks about connection of Classical and Quantum mechanics

[OldMark]

In my first posts I'd tried to attract attention to the idea that in proving of Classical and Quantum pictures of Nature more complicated is the clasical one. As I think nobody understood me. As an example you can take an idea of the material point. But more important is the next: In Hamiltonian's formalism in CM they describe physics picture through two groups of variables (q, t; p, E), which are Fourier conjugate ones. From compleetness of 4-dimensional Fourier transform it follows that for full describing a physical system it is enough only one of the variables set. Thus, you cannot simultaniously to set the both groups. In QM it is fulfiled by the Uncertainty principle. In CM only limitation is the Hamiltonian's minimal action principle. My statement is that the principle is the above mentioned limitation. Indeed, Hamiltonian's function (in CM) is an integral kernel of infinitesimal time shift. In the case, Hamilton's function plays the same role as the Fourier transform kernel.

[Frink]

Ummm.... yeaaah.

[OldMark]

I'm coming back for this thread for clearing of my idea. QM was created as a way of explanation of experimental results. As a proof of validity of QM was the fact of limit transition to CM as a de Broil's wavelength tends to zero. My point of view is that some picturesque objects of CM themselves have inner contradictions, which naturally can be overcome by help the QM. From this point of view the correspondence theorem has a natural explanation. As to the contradictions of CM I mark two: A mecanical system can be described by each from two set of parametrs: q, t or p,E which are connected 4-dimensional Fourier transform. Thus, the action (S) is not a state function, but it is connected with an integral operator of the Fourier transform exp(iS). So f(q,t) or f1(p,E)=F(f(q,t)) are the state functions of the system in different presentations. As to the second contradictions it is an idea of the material point. Space Fourier transform of the material point is infinitive. So we can't consider the object as physical object and have to go to space density.