Uncertain principle and Noether theorem?

[ndung200790]

Please teach me this:
It seem Noether theorem say that a symmetry corespondant a conservation observation at classical level, and at quantum framework the uncertain principle works.So I don't understand why at quantum level,there still exist conservation law.Example momentum conservation at vertex of Feymann diagram.
Thank you very much in advance.

 

[dextercioby]

Well, if an observable A is conserved, then its commutator with the Hamiltonian is zero, thus we can say that $\Delta A \dot \Delta H \geq 0$ on all the common domain. That's all to it.

 

[ndung200790]

So,are there any relation between symmetry and conservation observations in quantum mechanics(beside the claim: if A is conserved , A must be to commute with H)?

 

[dextercioby]

If A implements a symmetry in the sense of Wigner and Weyl, then A is conserved which means that A commutes with H on all the common domain, of course, assuming the explicit time independence of A in the Schroedinger picture,