# Conservative physical quantities

1. Aug 23, 2015

### 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

2. Aug 23, 2015

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

3. Aug 23, 2015

### KostasV

i am concerned about the components !
Ok, lets 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 ?

4. Aug 23, 2015

### 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.

5. Aug 23, 2015

### KostasV

Thank you very much for the help ;)