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!

Quantum Rigid Rotor

  1. Apr 16, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider a rigid rotor with moment of inertia Ix = Iy = I, Iz = (1 + ε)I
    Classically, his energy is given by, E = L^2/2I.

    (c) What are the new energy eigenstates and eigenvalues?
    (d) Sketch the spectrum of energy eigenvalues as a function of ε. For what sign of do the energy eigenvalues get closer together? Intuitively, why?
    (e) What is the degeneracy of the nth energy eigenvalue? Is the degeneracy fully lifted? If so, explain why and suggest a way to break only some of the degeneracy. If not, explain why not and suggest a way to break all of the degeneracy.

    2. Relevant equations



    3. The attempt at a solution

    So I know that in the spherically symmetric case, the eigenstates are spherical harmonics with eigenvalues of hbar^2/2I * l(l+1) and the degeneracy is given by 2l+1...but I was sort of just given that--I mean it makes sense, but I didn't have to solve a differential equation, so I am unsure how to proceed here, particularly (c)...
     
  2. jcsd
  3. Apr 17, 2013 #2

    DrClaude

    User Avatar

    Staff: Mentor

    Can you write down the Hamiltonian for the rigid rotor?
     
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: Quantum Rigid Rotor
  1. Quantum Rigid Rotator (Replies: 2)

Loading...