On a solution of the Schrodinger equation with a hyperbolic double-well   potential
  We report a solution of the one-dimensional Schrodinger equation with a hyperbolic double-well confining potential via a transformation to the so-called confluent Heun equation. We discuss the requirements on the parameters of the system in which a reduction to Heun polynomials is possible, representing the wavefunctions of bound states. 
C. A. Downing
math-ph math.MP quant-ph