Group analysis of Schroedinger equation with generalised Kratzer type potential

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.