Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Conservative physical quantities

  1. Aug 23, 2015 #1
    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. jcsd
  3. Aug 23, 2015 #2

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
  4. Aug 23, 2015 #3
    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 ?
     
  5. Aug 23, 2015 #4

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    In that case, where the one which commutes the Hamiltonian is the vector L, the components all commute with the Hamiltonian as well.
     
  6. Aug 23, 2015 #5
    Thank you very much for the help ;)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook