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In this communication, we present an efficient method for computation ofenergy and wave function of weakly bound nuclei by the application ofsupersymmetric quantum mechanics (SSQM) and bound states in continuum (BIC)technique. As a case study the scheme is implemented to the two-body ($^{30}$Ne+ n) cluster model calculation of neutron-rich nucleus $^{31}$Ne. Woods-Saxoncentral potential with spin-orbit component is used as the core-nucleoninteraction. The two-body Schr\"{o}dinger equation in relative coordinate issolved numerically to get the energy and wave function of the low-lying boundstates. A one-parameter family of isospectral potential (IP) is constructedfrom the bound state solutions following algebra of SSQM to find energies andwave functions of the resonance states. In addition to the 2p$_{3/2^-}$ (-0.33MeV) ground state, two bound excited states: s$_{1/2}$ (-0.30 MeV), $p_{1/2}$(-0.15 MeV) are also obtained. Few low-lying resonance states: f$_{7/2_1}$(2.57 MeV), f$_{7/2_2}$ (4.59 MeV), f$_{5/2_1}$ (5.58 MeV), p$_{1/2_1}$(1.432MeV), p$_{1/2_2}$ (4.165 MeV), p$_{3/2_1}$ (1.431 MeV), p$_{3/2_2}$ (4.205 MeV)are predicted. Among the predicted resonance states, the f$_{7/2^{-}}$ statehaving resonance energy $E_R \simeq 4.59$ MeV is in excellent agreement withthe one found in the literature.

Resonance energy and wave functions of $^{31}$Ne: a calculation using supersymmetric quantum mechanics