Quantum Rigid Rotor Homework: Energy Eigenstates & Degeneracy

[black_hole]

Homework Statement

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.

Homework Equations

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)...

 

[DrClaude]

Can you write down the Hamiltonian for the rigid rotor?