Phase shifts produced by two supersymmetric partner potentials satisfy a simple relation. One expects that the phase shift can be obtained algebraically, if the potential is shape invariant. We show that this is true only for a special class of shape invariant potentials. Among known shape invariant potentials, only the Coulomb potential satisfy this requirement. The Coulomb phase shift can be obtained analytically, which agrees with the well-known standard result.

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We have used a novel theoretical technique to calculate the 5 2 + resonance state of 11 Be using a two-body model ( 10 Be+n). The effective two-body potential for the system has a shallow well followed by a low and very wide barrier causing numerical difficulties in the calculation of low-lying resonances. Using supersymmetric quantum mechanics (SSQM), one can construct an isospectral potential with a bound state in the continuum (BIC). This isospectral potential has a deep well and high barrier which can effectively trap the system giving rise to a BIC. Our calculated resonance energy of the 5 2 + state of 11 Be matches extremely well with the experimental value. Calculated width of the resonance also agrees within the computational error bars.

Tunneling through a triple finite square barrier is examined in the light of WKB and supersymmetric WKB (SWKB) method. We have studied the quasi-bound states using lowest order WKB and SWKB quantization condition. The resonance energies have a doublet structure which represents a twofold quasi-degeneracy as expected from the symmetry of the three barriers enclosing two identical trapping regions. For very closely spaced low-lying resonance doublets, we find that the SWKB method gives much improved results than the conventional WKB method.

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