Exact polynomial eigensolutions of the Schrödinger equation for the pseudoharmonic potential

The polynomial solution of the Schrödinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum l. The exact bound-state energy eigenvalues and the corresponding eigenfunctions 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.