Calculation of state energy of (2n+1)-fold wells using the spectral properties of supersymmetry shape-invariant potential

Shape invariance is an important factor of many exactly solvable quantum mechanics. Several examples of shape-invariant ‘discrete quantum mechanical systems’ are introduced and discussed in some detail. We present the spectral properties of supersymmetric shape-invariant potentials (SIP). Here we are interested in some time-independent integrable systems which are exactly solvable owing to the existence of supersymmetric shape-invariant symmetry. In 1981 Witten proposed (0+1)-dimensional limit of supersymmetry (SUSY) quantum field theory, where the supercharges of SUSY quantum mechanics generate transformation between two orthogonal eigenstates of a given Hamiltonian wit degenerate eigenvaluesfor the non-SIP as very few lower eigenvalues can be known analytically, which are small to calculate spectral fluctuation.