(a) Calculate the energy eigenvalues of an axially symmetric rotator and find the degeneracy of each energy level (i.e., for each value of the azimuthal quantum number m, find how many states ∣lm⟩ correspond to the same energy). We may recall that the Hamiltonian of an axially symmetric rotator is given by
H^=2I1L^x2+L^y2+2I2L^z2,
where I1 and I2 are the moments of inertia.
(b) From part (a) infer the energy eigenvalues for the various levels of l=3.
(c) In the case of a rigid rotator (i.e., I1=I2=I), find the energy expression and the corresponding degeneracy relation.
(d) Calculate the orbital quantum number l and the corresponding energy degeneracy for a rigid rotator where the magnitude of the total angular momentum is 56ℏ.