Simple supersymmetric recipe for calculating the vibrational–rotational levels of a diatomic molecule

The methods of supersymmetric quantum mechanics are applied to the energy eigenvalue problem of a rotating oscillator. A uniform analytic expression for the superpotential is proposed, which can be used for almost any confining potential around its minimum. It is demonstrated that the long-range part of all supersymmetric partner potentials can be determined exactly. Combining these general results, it is possible to construct the whole hierarchy of partner potentials analytically. This, in turn, enables to accurately ascertain all discrete and quasi-discrete energy levels of an arbitrary rotating oscillator without solving the Schrِdinger equation.