  We consider the radial Schr\" odinger equation with the pseudo-Gaussian
potential. By making an ansatz to the solution of the eigenvalue equation for
the associate Hamiltonian, we arrive at the general exact eigenfunction. The
values of energy levels for the bound states are calculated along with their
corresponding normalized wave-functions. The case of positive energy levels,
known as meta-stable states, is also discussed and the magnitude of
transmission coefficient through the potential barrier is evaluated.
