  Using the method of $su(1,1)$ spectrum generating algebra, we analyze one
dimensional Schroedinger equation with potential in the form ${C\over{x^2} +
{D\over{x}}$ to obtain a class of potentials giving similar eigenvalues. By a
group analysis of the differential equation it is found that the symmetry gets
enhanced for particular values of $C$ and $D$. The generators of the Lie
algebra do not close. The extension of the vector field gives rise to an
interesting algebra.
