Rigid diatomic polar molecules in an external uniform electric field

This paper presents a didactic treatment of the rigid diatomic molecule under the action of an external electric field. We discuss the role of a new constant of motion that is valid when the electric field breaks spherical symmetry. We obtain the wave functions and the energies in the radial direction as well as the angular degrees of freedom, the latter corresponding to the eigenvalue spectrum of the new constant of motion. We apply the theory of the HBr molecule, and plot some of its eigenfunctions to show how they deform under the presence of an electric field. We calculate the wave lengths of the absorbed electromagnetic radiation in the transition of the first and second excited states and with different field values.