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!

E-field Perturbation of 2D rotor. Show Y_10 couples ground state?

  1. Oct 13, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider a molecule with an electric dipole moment d. The Hamiltonian of a molecule in the external electric field E is: [itex]\hat{H} = \frac{\hat{L^2}}{2I} - dE \cos{\theta}[/itex], where the polar angle [itex]\theta[/itex] characterises the orientation of the molecule. (We have chosen the field direction as the angular momentum quantisation axis.) Let us find field-induced contribution to the ground-state energy.

    Consider the action of the perturbation operator [itex]\hat{V} = −dE \cos{\theta}[/itex] on the ground-state wave function [itex]Y_{00}[/itex]. How does the function [itex]Y_{00}[/itex] depend on angles? Use this to show that there is only one state which is coupled to the ground state by [itex]\hat{V}[/itex], the state with [itex]\ell = 1[/itex] and [itex]m = 0[/itex].

    2. Relevant equations

    3. The attempt at a solution

    I have stated that [itex]Y_{00}[/itex] does not depend on angles, but have no idea how to show that [itex]Y_{10}[/itex] is the only state that couples with the ground state.
  2. jcsd
  3. Oct 13, 2013 #2


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    What does it mean mathematically to say that a state ##Y_{l,m}## is coupled to the ground state ##Y_{0,0}## by ##\hat{V}##?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: E-field Perturbation of 2D rotor. Show Y_10 couples ground state?