Hmm well this question isn't general except in the sense that I have no idea about how to solve it and hence have no idea what physics it involves! Two particles particle one obeys H_1 = (p_1)^2/(2m_1) + V1(r_1) particle two obeys H_2 = (p_2)^2/(2m_2) + V2(r_2) The system obeys H = H_1 + H_2 + V(|r1 - r2|) (the latter is the relative distance between the two particles' positions) r_1 and r_2 are scalars, r1 and r2 are the respective vectors 1.) Find an operator that commutes with H_1 and state its equation of motion 2.) Find an operator that commutes with H_2 and state its equation of motion 3.) Find an operator that commutes with H (and prove that it does) How do I go about doing this? I can only think of trivial examples, like H_2 commutes with H_1 and vice-versa, and nothing for H. There is no other information given, so I can't assume this is the helium atom or something.