Exact Polynomial Eigensolutions of the Schrodinger Equation for the   Pseudoharmonic Potential
  The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically calculated. The energy states for several diatomic molecular systems are calculated numerically for various principal and angular quantum numbers. By a proper transformation, this problem is also solved very simply by using the known eigensolutions of anharmonic oscillator potential. 
Sameer M. Ikhdair and Ramazan Sever