In general, a system of quantum particles can never behave even approximately like a rigid body, but non-spherical nuclei and molecules are exceptions, and have certain rotational energy levels that are well described as states of a rigid rotator whose Hamiltonian is 21 %3D where I is the moment of inertia, and L^ is the angular momentum operator. a, What are the eigenvalues of the angular momentum operator? b. A rigid rotator with Hamiltonian (6) is subjected to a constant perturbation V = (Ch² /21) cos² 0. , where C is a small constant. Find the corrections to the eigenvalues and eigenfunctions to first order in perturbation theory. c. Given the perturbation condition in (b.), estimate the maximum value of C for which this is a good approximation for the level characterized by the quantum number l

In general, a system of quantum particles can never behave even approximately like a rigid body, but non-spherical nuclei and molecules are exceptions, and have certain rotational energy levels that are well described as states of a rigid rotator whose Hamiltonian is 21 %3D where I is the moment of inertia, and L^ is the angular momentum operator. a, What are the eigenvalues of the angular momentum operator? b. A rigid rotator with Hamiltonian (6) is subjected to a constant perturbation V = (Ch² /21) cos² 0. , where C is a small constant. Find the corrections to the eigenvalues and eigenfunctions to first order in perturbation theory. c. Given the perturbation condition in (b.), estimate the maximum value of C for which this is a good approximation for the level characterized by the quantum number l