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The theoretical procedure of supersymmetric quantum mechanics (SQM) isadopted for the first time to study quasi-bound states of a weakly boundnuclear system using microscopic potential. The density dependent M3Y (DDM3Y)effective interaction was found earlier to give a satisfactory description ofradioactivity, nuclear matter and scattering. In the present work, we havegenerated a two-body potential microscopically in a single folding model usingthe DDM3Y effective interaction. From this potential, SQM generated a family ofisospectral potentials for $^{11}$Be ($^{10}$Be + n). We investigated the5/2$^+$, 3/2$^-$ and 3/2$^+$ resonance states of $^{11}$Be. The experimentaldata and the present calculations of excitation energies of the above resonancestates are found to be in good agreement.

Study of resonance states of $^{11}$Be with isospectral bound state microscopic potential