Perturbative expansion of the energy eigenvalues for the planar quantum rotor based on the calculation of a finite degree secular polynomial

The free planar rotor system is introduced and the interaction of this system with an external electric field is studied. The quantum problem is governed by an equation of Mathieu type. This is done by evaluating a finite secular polynomial corresponding to a matrix representation of the Hamiltonian for the system. It is shown that perturbative expansions for the energy can be evaluated in powers of the coupling constant.