Sample problem 2

Suppose the Hamiltonian of a rigid rotator in the magnetic field perpendicular to the axis is of the form(Merzbacher 1970, problem 17-1)

$H=AL^{2}+BL_{z}+CL_{y}$

if terms quadratic in the field are neglected. Assuming B, use Pertubation to the lowest nonvanishing order to get approximate energy eigenvalues