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

Commutation Relationships and Operator Functions

  1. Nov 3, 2012 #1
    There are 2 operators such that [A,B] = 0. Does [F(A),B]=0 ?

    Specifically, lets say we had the Hamiltonian of a 3-D oscillator H and L^2. We know that L^2 = Lx^2+Ly^2+Lz^2, and it is known that [H,Lz] = 0. Can we say that since H and Lz commute, H and Lz^2 also commute, by symmetry H and Lx^2,Ly^2 commute also and therefore H and L^2 commute?
     
  2. jcsd
  3. Nov 3, 2012 #2
    If the Taylor expansion of [itex]F(A)[/itex] converges, then you can essentially assume that it is a polynomial in [itex]A[/itex], so it will commute. Your argument about [itex]H[/itex] and [itex]L^2[/itex] sounds right.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Commutation Relationships and Operator Functions
  1. Operators Commutation (Replies: 6)

  2. Commutator of operators (Replies: 15)

Loading...