  The theoretical procedure of supersymmetric quantum mechanics (SQM) is
adopted for the first time to study quasi-bound states of a weakly bound
nuclear system using microscopic potential. The density dependent M3Y (DDM3Y)
effective interaction was found earlier to give a satisfactory description of
radioactivity, nuclear matter and scattering. In the present work, we have
generated a two-body potential microscopically in a single folding model using
the DDM3Y effective interaction. From this potential, SQM generated a family of
isospectral potentials for $^{11}$Be ($^{10}$Be + n). We investigated the
5/2$^+$, 3/2$^-$ and 3/2$^+$ resonance states of $^{11}$Be. The experimental
data and the present calculations of excitation energies of the above resonance
states are found to be in good agreement.
