  A method based on supersymmteric (SUSY) quantum mechanics has been developed
by exploiting conditional Shape invariance property for obtaining exact ground
state solution of generalized polynomial potential with Coulomb term. Specific
cases have been discussed with extensive analytical calculation. How this
method can be used to calculate the excited states has also been demonstrated.
We have also used a numerical technique (RKGS) and obtained the energy
eigenvalues upto second excited state by solving the Schrodinger equation for
quartic and sextic polynomial potentials with the Coulomb term and shown that
the analytical results provide very good approximations to the numerical
results.
