1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dependence of potential on only the *difference* between two variables

  1. Aug 5, 2009 #1
    I'm reading a paper that considers a diatomic molecule living in two dimensions in which the central nucleus is fixed at the origin. Ignore the electrons for the time being. Let [itex](r_1,\theta_1)[/itex] and [itex](r_2,\theta_2)[/itex] describe the locations of the nuclei, and let the molecule be subject to a potential [itex]V(r_1,r_2,\theta_1,\theta_2)[/itex]. The paper claims that, if the potential is the same when we rotate the entire molecule, we must have
    V(r_1,r_2,\theta_1,\theta_2) = V'(r_1,r_2,\theta_2-\theta_1);
    i.e., the potential only depends on the difference between [itex]\theta_1[/itex] and [itex]\theta_2[/itex]. So the potential really only depends on three variables: [itex]r_1[/itex], [itex]r_2[/itex], and [itex]\phi[/itex], where [itex]\phi = \theta_2 - \theta_1[/itex]. Can someone please explain why this is? I don't see it.
  2. jcsd
  3. Aug 8, 2009 #2
    what are the angle representative of?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook