Conservative physical quantities

[KostasV]

Hello ppl !
If i find that a physical quantity (lets say angular momentum operator vector L) is conservative (this means [H,L]=0 - H=hamiltonian ) then its 3 components Lx , Ly and Lz are being conserved too ?
That happens with every conservative vector operator ? Like spin vector S and his components?
I am confused ... :S

 

[blue_leaf77]

The constants of the motion is dependent on the Hamiltonian, for simple Hamiltonian such as hydrogen atom whose potential is symmetric, angular momentum L and its components are indeed conserved in time.

That happens with every conservative vector operator ?

Its the Hamiltonian which decides whether an operator is conserved in time or not.

 

[KostasV]

The constants of the motion is dependent on the Hamiltonian, for simple Hamiltonian such as hydrogen atom whose potential is symmetric, angular momentum L and its components are indeed conserved in time.

Its the Hamiltonian which decides whether an operator is conserved in time or not.

i am concerned about the components !
Ok, let's say that i find that [H,L]=0 (so L -angular momentum vector- is being conserved) ! Do i have to find the commutators [H,Lx] , [H,Ly] , [H,Lz] or i am sure that they will all be zero due to the fact that [H,L]=0 ?

 

[blue_leaf77]

In that case, where the one which commutes the Hamiltonian is the vector L, the components all commute with the Hamiltonian as well.

 

[KostasV]

In that case, where the one which commutes the Hamiltonian is the vector L, the components all commute with the Hamiltonian as well.

Thank you very much for the help ;)