Novel quasi-exactly solvable models with anharmonic singular potentials

We present new quasi-exactly solvable models with inverse quartic, sextic, octic and decatic power potentials, respectively. We solve these models exactly by means of the functional Bethe ansatz method. For each case, we give closed-form solutions for the energies and the wave functions as well as analytical expressions for the allowed potential parameters in terms of the roots of a set of algebraic equations.

► The quasi-exactly solvable treatments of a class of singular anharmonic models. ► Exact solutions to a class of integer power singular potential. ► Solutions obtained in terms of the roots to the Bethe ansatz equations. ► Results useful in describing diatomic molecules and elastic differential cross sections for high energy scattering.