Series solution of a central potential problem with three-term recursion   relation
  The series solution of the radial part of the Schr\"odinger equation for simultaneous coulomb and harmonic potential involves three-term recursion relation and is thus difficult to solve for bound states. We have suggested a simple method to solve for low lying states. Finite polynomial solutions exist only if the coulomb and oscillator potentials are nontrivially related. 
Jishnu Goswami, Chandan Mondal and Dipankar Chakrabarti
math-ph math.MP quant-ph