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 via 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 a set of algebraic equations. 
Davids Agboola and Yao-Zhong Zhang
math-ph hep-th math.CA math.MP nlin.SI quant-ph